diff --git a/README.md b/README.md
index 82577f1..654077a 100644
--- a/README.md
+++ b/README.md
@@ -16,7 +16,7 @@ afem/
│ ├── mesh_refinement.py # ★ 核心：网格细化 RL 环境
│ │ # - GNN 图观测构建（节点 + 边特征）
│ │ # - continuous_sizing_field (score-based + budget) 细化策略
-│ │ # - spatial 奖励
+│ │ # - spatial 奖励 + step0 penalty 降权
│ ├── helmholtz.py # Helmholtz FEM 求解器 + 残差误差估计
│ ├── fem_problem.py # FEM 问题封装 + PDE 循环缓冲区
│ ├── fem_util.py # 三角形面积、中点、随机采样、尺寸场函数
@@ -46,7 +46,7 @@ afem/
- **边界条件**: SBC (Sommerfeld) `∂u/∂n = i·k·u`
- **域**: 可配矩形域，初始网格密度自适应 + domain area 线性缩放：`N_init = N_base × (k/k_ref)^k_exponent × domain_area`。k_ref 和 k_exponent 均可通过 helmholtz config 配置（默认 k_exponent=2.0, k_ref=6.0），保证不同域尺寸下每单位面积单元数一致
- 可配 exponent：^2 = P1 Helmholtz 理论最优 (污染误差 ∝ k²)。建议 N_base 配合 exponent 调整，使 N_init 约为 COMSOL 目标 (λ/10√ε_r) 的 30-50%，为 RL agent 留出充分细化空间
-- **介质区前渐近区边缘约束**: 介质内 λ_d = 2π/(k√ε_r) 更短，强制迭代细化至 h ≤ λ_d/N（默认 N=1.5，helmholtz.pre_asymptotic_N 可配）。约 1.5 点/波长，刚好跨过渐近区门槛，赋予初始网格基本相位解析能力但不过度消耗物理预算，为 RL agent 留出充分的选择性细化空间
+- **介质区前渐近区边缘约束**: 介质内 λ_d = 2π/(k√ε_r) 更短，强制迭代细化至 h ≤ λ_d/N（默认 N=2.0，helmholtz.pre_asymptotic_N 可配）。约 2 点/波长，赋予初始网格基本相位解析能力但不过度消耗物理预算，为 RL agent 留出充分的选择性细化空间
- **后验误差**: 残差型 indicator（Ainsworth & Oden 风格），含单元内部残差 + 梯度跳变 + SBC 边界残差
### 强化学习建模
@@ -54,29 +54,80 @@ afem/
| 概念 | 对应实体 |
|------|---------|
| **智能体** | 每个三角形网格单元 |
-| **状态** | GNN 节点特征（几何 + PDE 残差 + 振幅 + 相位方向 + 物理参数，节点 13 维 + 边 1 维） |
-| **动作** | 1 维连续标量 x_i → score = -x_i 排序，在物理预算内 top-k 选细化单元（x 越小优先级越高） |
-| **奖励** | 局部子单元 η 的 log-ratio 改善（spatial: sum 聚合 / spatial_max: max 聚合）+ α 衰减全局 η log-ratio shaping |
-| **终止** | 达到最大步数或超过最大单元数 |
+| **状态** | GNN 节点特征（几何 + PDE 残差 + 振幅 + 相位方向 + 物理参数，节点 13 维 + 边 1 维） + 13 维全局统计向量 |
+| **动作** | 1 维连续标量 δ_i → `score_i = log(η_i + ε) + c·tanh(δ_i)` 降序 top-k 选择（η baseline + bounded Actor correction） |
+| **奖励** | 纯局部 r_local = log(η_old) − log(l2(η_child))，clip [0, 2.0]，减去动作惩罚（step0 降权）；未细化单元 r=0 |
+| **终止** | 达到最大步数、超过最大单元数、或 sel=0（无单元可选） |
---
## 网络架构
-双 GNN 架构（policy / value 各自独立基座）：
+双流 GNN 架构（Actor / Critic 共享基座，各自独立头）：
```
-图观测 → MessagePassingBase → MLP → 动作分布 / value 标量
- ├─ nn.Linear（嵌入）
- ├─ MessagePassingStack（2 层消息传递 + GVN 全局广播，inner 残差 + LayerNorm）
- │ ├─ MessagePassingStep × N
+图观测 → MessagePassingBase → Actor MLP → δ_i (连续动作)
+ ├─ nn.Linear（嵌入） → Critic MLP → V(s) (标量)
+ ├─ MessagePassingStack（2 层消息传递 + MultiPoolGVN 全局广播）
+ │ ├─ MessagePassingStep × 2
│ │ ├─ EdgeModule: MLP([src | dst | edge_attr])
│ │ └─ NodeModule: MLP([node | scatter(入边)])
- │ └─ GlobalVirtualNode (GVN): η_K 加权注意力池化 → 注意力门控广播
- │ h_V = Σ(η_v/Ση)·h_v，α_v = σ(W_att[h_v || h_V])，h_v ← h_v + α_v ⊙ W_V·h_V
- └─ 输出: 节点隐向量
+ │ │ 内残差 + LayerNorm
+ │ └─ MultiPoolGVN: 多策略池化 + 13 维全局统计 → 注意力门控广播
+ │ Stage A: g_global = MLP(concat(g_mean, g_eta, global_stats))
+ │ Stage B: α_v = σ(W_att[h_v || g_global])
+ │ h_v ← h_v + scale · α_v ⊙ W_V · g_global
+ └─ 输出: 节点隐向量 h_i
+
+Actor 输入: concat(h_i, g_global, rel_logeta, rel_area, is_top_eta, budget_stats) [2D+6]
+Critic 输入: concat(h_i, g_global) [2D]
```
+### MultiPoolGVN — 多池化全局虚拟节点
+
+替代原始单一 η 加权 GVN，用多种池化策略聚合节点嵌入，拼接全局统计后生成 `g_global`：
+
+| 池化模式 | 公式 | 说明 |
+|----------|------|------|
+| `mean` | `g_mean = Σ h_v / N` | 均匀平均 |
+| `eta_softmax` | `g_eta = Σ (η_v / Ση) · h_v` | η 加权 softmax，高误差节点主导 |
+| `top_eta` | `g_top = mean(h_v : log η_v > μ + σ)` | top-η 节点均值（log 空间 >1σ） |
+
+配置项 `gvn_pooling: [mean, eta_softmax]`，可选加 `top_eta`。
+
+### Global Stats — 13 维图级统计
+
+每个图观测附带 13 维全局统计向量（`graph.global_stats`），用于 GVN 和 Actor/Critic 的条件输入：
+
+| 索引 | 名称 | 说明 |
+|------|------|------|
+| 0 | `remaining_ratio` | (N_budget − N_current) / N_budget |
+| 1 | `step_ratio` | current_step / max_steps |
+| 2 | `elem_ratio` | N_current / N_budget |
+| 3 | `logeta_mean` | log(η) 均值 |
+| 4 | `logeta_std` | log(η) 标准差 |
+| 5 | `logeta_max` | log(η) 最大值 |
+| 6 | `logeta_p90` | log(η) P90 |
+| 7 | `logeta_p75` | log(η) P75 |
+| 8 | `top10_eta_energy` | top 10% η² 能量占比 |
+| 9 | `eligible_ratio` | 面积安全阈值以上元素占比 |
+| 10 | `inside_eta_energy` | 散射体内 η² 能量占比 |
+| 11 | `outside_eta_energy` | 散射体外 η² 能量占比 |
+| 12 | `interface_eta_energy` | 界面附近 η² 能量占比 |
+
+### 全局条件化 Actor/Critic
+
+当 `use_global_conditioned_correction: true` 时，Actor 和 Critic 的输入额外拼接全局上下文：
+
+- **Actor**: `concat(h_i, g_global, rel_logeta, rel_area, is_top_eta, budget_stats)` → 维度 `2D + 6`
+ - `rel_logeta`: `(log η_i − μ) / σ`，per-graph 标准化
+ - `rel_area`: `log(area_i / mean_area)`，per-graph 相对面积
+ - `is_top_eta`: `rel_logeta > 1.0` 的 0/1 标记
+ - `budget_stats`: `[remaining_ratio, step_ratio, elem_ratio]`
+- **Critic**: `concat(h_i, g_global)` → 维度 `2D`
+
+### 超参数
+
| 超参数 | 值 |
|--------|-----|
| latent_dim | 64 |
@@ -86,18 +137,23 @@ afem/
| 边 dropout | 0.1 |
| Actor MLP | 2 层 tanh |
| Critic MLP | 2 层 tanh |
-| Optimizer | Adam, lr=3e-4, lr_decay=0.995 |
-| **动作分布** | `DiagGaussianDistribution`（连续 Box 动作空间），`log_std` 可学习，clamp 在 [-4.0, -1.0] |
-| **log_std 策略** | 初始化 -2.0（std≈0.135），每步 optimizer.step() 后 clamp 到 [-4.0, -1.0]（std ∈ [0.018, 0.368]），熵系数 0.001 |
+| Optimizer | Adam, lr=3e-4, lr_decay=1.0 |
+| **动作分布** | `DiagGaussianDistribution`（连续 Box 动作空间），`log_std` 可学习，clamp 在 [-2.5, -1.0] |
+| **log_std 策略** | 初始化 -2.0（std≈0.135），每步 optimizer.step() 后 clamp 到 [-2.5, -1.0]（std ∈ [0.082, 0.368]），熵系数 0.01 |
+| **correction_scale** | 0.3 — Actor 修正幅值 c·tanh(δ) ∈ [−0.3, +0.3] |
+| **correction_reg_coef** | 0.03 — correction 正则化系数，L_corr = coef × mean(correction²) |
+| **step0_penalty_scale** | 0.3 — 第一步 element penalty 降权系数 |
### 动作分布策略说明
环境定义的是 `_action_space`（下划线前缀），网络初始化时必须用 `environment._action_space` 而非 `environment.action_space`（后者默认为 None，会错误回退到 `CategoricalDistribution(1)`，导致 policy gradient 恒为零）。
-`continuous_sizing_field`（score-based）的动作有效范围约 [-3, 3]：
-- score = -x_i，x 越小 ⇒ 优先级越高（纯排序，不设正负门槛）
-- `initial_log_std=-2.0`（std≈0.135），clamp 在 [-4.0, -1.0]（std ∈ [0.018, 0.368]）
-- 加 `entropy_coefficient=0.001` 提供微弱探索压力，避免 log_std 过早收敛到下限
+`continuous_sizing_field`（score-based）的 scoring 公式：
+- `score_i = log(η_i + ε) + c·tanh(δ_i)`，其中 c=`correction_scale`
+- Actor 输出 δ_i，经 tanh 限幅，只能微调 log(η) 基准排序，不能覆盖物理先验
+- 选 top-k 按 score 降序（越大越优先）
+- `initial_log_std=-2.0`（std≈0.135），clamp 在 [-2.5, -1.0]（std ∈ [0.082, 0.368]）
+- `entropy_coefficient=0.01`
---
@@ -152,7 +208,8 @@ main.py --mode train/test/viz
└─ train_step() # 多 epoch PPO 更新
├─ policy_loss() # Clipped PPO
├─ value_loss() # Clipped value loss
- └─ entropy_loss() # 熵正则
+ ├─ entropy_loss() # 熵正则
+ └─ correction_reg() # Correction 正则化 L_corr
```
### 环境内部调用
@@ -163,16 +220,15 @@ MeshRefinement.reset()
└─→ initial_mesh (meshpy → 介质内 前渐近区边缘迭代细化)
MeshRefinement.step(action)
- ├─→ score = -x 排序 + 物理预算约束 → top-k 细化单元
+ ├─→ score = log(η) + c·tanh(δ) 排序 + 物理预算约束 → top-k 细化单元
├─→ FEMProblemWrapper.refine_mesh() # scikit-fem refine
├─→ calculate_solution_and_get_error()
│ ├─→ HelmholtzProblem.calculate_solution() # FEM 求解
│ └─→ _compute_residual_indicator() # 残差误差
- ├─→ _get_reward_by_type() # spatial 奖励
- └─→ last_observation # 构建 Data(x, edge_index, edge_attr)
+ ├─→ _get_reward_by_type() # spatial 奖励 + step0 penalty 降权
+ └─→ last_observation # 构建 Data(x, edge_index, edge_attr, eta, area, global_stats)
```
-
### 训练
```bash
@@ -182,16 +238,25 @@ CUDA_VISIBLE_DEVICES=7 python src/main.py --mode train --config src/config.yaml
首次迭代需收集 256 步 rollout（含 FEM 求解），后续打印：
```
-it | loss ev agents reward x<0 elig sel time
+it | loss ev agents avg_r sum_r corr_m corr_s r_le_sc δ<0 elig sel rem_r corr_reg corr_l2 corr_a p_sc avg_p avg_rl step_id time
```
| 字段 | 含义 | 健康范围 |
|------|------|---------|
-| `x<0` | `mean(x_i < 0)`，负值动作比例（纯诊断） | 越负的单元优先级越高 |
-| `elig` | 通过双过滤器的候选占比 | 排除数值退化 + 低误差的单元 |
-| `mask` | 被 Reverse Dörfler 剔除的噪声尾部占比（累积能量 <1% 总误差的底部单元） | 因场景而异，非固定比例 |
+| `corr_m` | `c·tanh(δ)` 均值 | 接近 0，Actor 修正无系统性偏差 |
+| `corr_s` | `c·tanh(δ)` 标准差 | 应稳定在 0.03–0.08，不应持续涨到 0.15 |
+| `r_le_sc` | Pearson r(log_η, score) | 接近 1.0 → Actor 修正小；<0.9 → Actor 在主动修正 |
+| `δ<0` | Actor 输出负值的比例（纯诊断） | — |
+| `elig` | 通过双过滤器的候选占比 | — |
| `sel` | 实际选中的细化单元数 | 每步最多 N_current // 4 |
-| `n_budget` | 全局物理预算（每 episode 固定） | k=30 → ~1800 |
+| `rem_r` | remaining / N_budget | — |
+| `corr_reg` | correction 正则化损失 L_corr | 监控 correction drift |
+| `corr_l2` | mean(correction²) | 监控 correction 幅值增长 |
+| `corr_a` | mean(\|correction\|) | 监控 correction 绝对值 |
+| `p_sc` | penalty_scale | step0=0.3，后续=1.0 |
+| `avg_p` | 平均 element penalty | step0 应明显小于后续 |
+| `avg_r_local` | 平均 r_local（penalty 前） | — |
+| `step_id` | 当前步数 | — |
### 测试
@@ -203,12 +268,12 @@ python src/main.py --mode test --checkpoint checkpoints/model_final.pt \
输出：
```
-Step 0: reward=--- error=1.0000 elements=174 budget=1885
-Step 1: reward=+12.345 error=0.7160 elements=618 x<0=0.45 sel=87
+Step 0: reward=--- aw_rel=79.28% max_err=2.2133 elements=1078 budget=...
+Step 1: reward=+2.345 aw_rel=30.10% max_err=0.7096 elements=2020 sel=269
...
```
-每步打印 `reward error elements x<0 sel`，第 0 步额外显示 `N_budget`。
+每步打印 `reward aw_rel max_err elements sel`，第 0 步额外显示 `N_budget`。
### 可视化
@@ -251,134 +316,52 @@ SBC 边界条件仍用 $k_{local}$（物理正确），仅归一化因子改用
### 连续尺寸场策略（score-based + 物理预算约束 + 动作掩码）
-Actor 输出标量 x_i → score = -x_i 直接排序，在预算和上限内选 top-k：
+Actor 输出标量 δ_i → `score_i = log(η_i + ε) + c·tanh(δ_i)`，在预算和上限内选 top-k：
```
-A_budget_i = ½(λ_local_i / 6)² // 每局部波长方向 ~6 尺度点（仅用于 N_budget 计算）
-λ_local_i = 2π / (k · √ε_r_i)
-
-N_budget = max(N_phys, ⌈5·N_init⌉) // rho_min=5.0，至少 5× 初始单元数，保证 RL 多步细化空间
-N_phys = ⌈ Σ |K_i| / A_budget_i ⌉ // 全局物理预算（k=30 真空 ~1800）
+ε = max(0.01·median(η), 1e-12) // 动态 eps，防止 log(0)
+corr_i = c · tanh(δ_i) c = correction_scale // Actor 修正幅值 ∈ [−c, +c]
+score_i = log(η_i + ε) + corr_i // 降序 top-k
+A_budget_i = ½(λ_local_i / 6)² // 每局部波长方向 ~6 尺度点（仅用于 N_budget）
+N_budget = max(N_phys, ⌈5·N_init⌉) // rho_min=5.0
remaining = N_budget − N_current
-V_min_safeguard = 1e-10 × domain_area // 纯数值底线（防止 FEM 求解器退化）
-eligible: area > V_min_safeguard AND η_K ∈ Reverse Dörfler 保留集 // 数值底线 + 能量尾部淘汰 (ε_noise=0.01, ≥20% floor)
+V_min_safeguard = 1e-10 × domain_area
+eligible: area > V_min_safeguard AND η_K ∈ Reverse Dörfler 保留集 (ε_noise=0.01, ≥20% floor)
num = min(|eligible|, N_current//4, remaining//3)
-selected = top-k by score = -x_i → 1-to-4 切分
+selected = top-k by score descending → 1-to-4 切分
```
-- score = -x_i：x 越小 ⇒ 优先级越高（纯排序，不设正负门槛）
-- 不再使用 `0.25·A_budget` 启发式面积地板：RL 应自主学会"细化到多细"，而非被人类经验 (12 点/波长) 限制。仅保留数值底线 V_min_safeguard = 1e-10 × domain_area 防止浮点精度问题。
-- per-step cap 从固定 200 改为自适应 `N_current // 4`，随网格规模缩放但增速更缓，避免大网格时单步消耗过多预算。rho_min 从 3.0 提升到 5.0，赋予更多预算余量。
-- **sel=0 提前终止**：当 agent 选中 0 个单元细化（预算耗尽或 Reverse Dörfler 屏蔽所有候选）时 episode 自动结束，不再浪费 FEM 求解
-- **k_exponent 可配**：初始网格缩放指数可通过 `helmholtz.k_exponent` 配置（默认 2.0），² 为 P1 Helmholtz 理论最优；对 k=30 的 $N_{init}$ 为 k=6 的 25× 倍
-- **动作掩码 (Reverse Dörfler)**：按 η_K 升序排列，剔除累积平方误差贡献 < ε_noise·Ση² 的底部单元（数值噪声/已收敛区）。基于能量分布而非密度分位数，在重尾和均匀误差分布下均自适应。保留率不低于 20% 确保 Agent 始终有充分的选择空间
+- Actor 通过 bounded correction 微调排序，不能覆盖物理先验 log(η)
+- Reverse Dörfler 动作掩码剔除噪声尾部，≥20% floor 确保 Agent 始终有选择空间
+- sel=0 提前终止：agent 选中 0 个单元时 episode 自动结束
+- k_exponent=2.0：P1 Helmholtz 理论最优初始网格缩放
### 奖励计算
----
-
-#### 变量
-
-| 符号 | 含义 |
-|------|------|
-| `η_K = √(r_int² + r_jump² + r_sbc²)` | 逐单元误差指示子，`r_*` 定义见式 (1)–(3) |
-| `C(i)` | 父单元 i 经 1-to-4 切分产生的子单元集合 |
-| `M_new[j]` | 子单元 j 对应的父单元索引 |
-| `n_i = |C(i)|` | 父单元 i 的子单元数（1 表示未切分） |
-| `E_global = √(Σ η_K²) / \|\|u_h\|\|_{L₂(Ω)}` | 全局无量纲误差 |
-
----
-
-#### 算法
-
-**Step 0 — 保存旧状态** (`_set_previous_step`)
+纯局部改善 reward，无调制、无 bonus：
```
-η_old ← 旧逐单元 η_K
-||u_h_old|| ← 旧解 L₂ 范数 (≈ √(Σ |ū_K|² · area_K))
+r_local_i = log(η_old_i + ε) − log(l2_η_children_i + ε)
+l2_η_children_i = √(Σ_{j∈C(i)} η_new_j²)
+
+reward_i = clip(r_local_i, 0, rmax) − penalty_scale · λ · (n_child_i − 1)
+
+rmax = 2.0
+λ = 0.02 (element_penalty.value)
+
+penalty_scale = step0_penalty_scale if current_step == 0 (默认 0.3)
+ = 1.0 otherwise
```
-**Step 1 — 网格细化** (`_refine_mesh`)
-
-```
-x = action.flatten()
-score = -x // x 越小 ⇒ 优先级越高
-
-remaining = N_budget − N_old
-max_by_budget = max(0, remaining // 3)
-// 数值底线 + Reverse Dörfler 能量尾部淘汰
-V_min_safeguard = 1e-10 × domain_area // 纯数值安全底线，防止 FEM 退化
-η_sq = η_old²; total_energy = Σ η_sq
-k_dorfler = searchsorted(cumsum(sort_asc(η_sq)), ε_noise·total_energy) // ε_noise=0.01
-k = min(k_dorfler, N − max(1, N//5)) // ≥20% floor
-eligible = {i | V_old[i] > V_min_safeguard AND i ∈ sort_asc_idx[k:] }
-num = min(|eligible|, N_old//3, max_by_budget)
-elements_to_refine = top-k of eligible by score
-
-M_new[j] ∈ {0,…,N_old-1} // 子→父映射
-```
-
-**Step 2 — FEM 求解 + 误差估计**
-
-```
-η_new ← 新逐单元 η_K
-||u_h_new|| ← 新解 L₂ 范数
-```
-
-**Step 3 — 因果奖励**（零和预算审查）
-
-ε_dynamic = max(0.01 × η_P95, 1e-6)
-
-// Refined parents: r_local + zero-sum bonus − penalty
-if i ∈ refined_parents:
- r_i = log(η_old + ε) − log(√(Σ η_child²) + ε) // r_local ≥ 0 (L₂ 聚合)
- + 0.3 × (η_old / μ − 1.0) // zero-sum bonus (Σ = 0)
- − 0.06 // action penalty
-
-// Unrefined parents: causal isolation
-else:
- r_i = 0
-
-> **零和奖金**：α·(η/μ−1) 全场求和为零。细化高于均值的单元得正奖金，低于均值的倒扣。
-> 这是 Dörfler 准则的 RL 对偶：Agent 必须选出误差超过全均水平的单元。
-> **因果隔离**：未细化单元 r ≡ 0。零和奖金本身足够强（介质内 +0.51）、
-> 不再需要忽视惩罚的推力，排序机制自动淘汰不划算的单元。
-> **L₂ 聚合**：√(Σ η_child²) ≤ η_parent 天然成立，r_local ≥ 0 永不惩罚细化。
-
-**Step 4 — 全局误差（仅诊断）**
-
-global_bonus = α·[log(E_old) − log(E_new)]，α = 0.5
-
-不注入 Actor reward。Helmholtz 污染误差可使 E_new > E_old 在正确细化后发生，
-注入 global_bonus 导致因果断裂。Actor 仅优化 Step 3 的 per-element reward。
-
----
-
-#### 奖励标度校准（旧尺寸场下测量，score-based 后需重新标定）
-
-在随机策略下实测各分量量级（1321 个 refined-parent 样本）：
-
-| 分量 | 均值 | 占 r_local 比例 |
-|------|------|:---:|
-| `r_local` (仅 refined parents) | +0.364 | — |
-| `penalty` λ·(n−1), λ=0.02 | +0.045 | 1/8 |
-| `α·ΔlogE` α=0.2 | +0.069 | 1/5 |
-| **net** | **+0.387** | |
-
-满足 `r_local ≫ penalty` 且 `α·ΔlogE ≈ r_local / 5`，局部 credit assignment 不被全局信号淹没。
-
----
-
-#### 设计要点
-
| 组件 | 聚合 | 作用 |
|------|------|------|
-| 局部项 `log(η_old / √(Σ η_child²))` | scatter_add，仅 refined parents | L₂ 保证 r_local ≥ 0；int 主导 +0.69 |
-| 零和奖金 `0.3×(η/μ−1)` | 仅 refined parents | Σ=0；高于 μ 得正奖，低于 μ 倒扣 (Dörfler 准则的 RL 对偶) |
-| 动作惩罚 `λ=0.06` | per-refined-parent | 轻微抑制网格膨胀（1-to-4 扣 0.06） |
-| 因果隔离 `r=0` | unrefined parents | 零和奖金足够强，不需额外推力 |
-| 全局项 `α·ΔlogE` α=0.5 | 仅诊断 | 不注入 Actor，避免污染误差因果断裂 |
+| 局部项 `log(η_old / √(Σ η_child²))` | scatter_add，仅 refined parents | L₂ 保证 r_local ≥ 0；clip 到 [0, 2.0] |
+| 动作惩罚 `λ=0.02` | per-refined-parent | 轻微抑制网格膨胀（1-to-4 扣 0.06） |
+| **step0 降权** | step 0 时 penalty × 0.3 | 防止第一步"真实误差改善但 reward 给负反馈" |
+| 因果隔离 `r=0` | unrefined parents | 未细化元素干净零基准 |
+
+**step0 penalty 降权动机**：诊断发现 step 0 经常出现 reward < 0 但真实 aw_rel 改善的情况，说明 element penalty 淹没了真实的物理改善信号。降权后 step 0 的 reward 与 Δaw_rel 符号一致性提高。
---
@@ -388,7 +371,185 @@ global_bonus = α·[log(E_old) − log(E_new)]，α = 0.5
- **奖励归一化**: rollout 内 reward 做 z-score 归一化（std < 1e-8 则跳过）
- **Value clipping**: 默认 clip_range=0.2
- **梯度裁剪**: max_grad_norm=0.5
-- **log_std clamp**: 每步 `optimizer.step()` 后将 `log_std` clamp 到 `[-3.0, -1.0]`，σ ∈ [0.05, 0.37]
+- **log_std clamp**: 每步 `optimizer.step()` 后将 `log_std` clamp 到 `[-2.5, -1.0]`，σ ∈ [0.082, 0.37]
初始化 `-2.0` (σ≈0.135)，放宽下限防止策略过早确定化
-- **熵正则**: `entropy_coefficient=0.005`，施加有意义的探索压力防止 x<0 崩塌
-- **epochs_per_iteration**: 3，减少对同一 rollout 的过拟合
+- **熵正则**: `entropy_coefficient=0.01`
+- **epochs_per_iteration**: 3
+
+### Correction 正则化
+
+为防止 Actor 学会利用"大 correction"刷局部 residual reward（correction drift / reward hacking），在 PPO loss 中加入 correction 正则项：
+
+```
+correction_i = correction_scale · tanh(action_i)
+L_corr = correction_reg_coef · mean(correction²)
+
+loss = policy_loss + value_coef · value_loss + entropy_coef · entropy_loss + L_corr
+```
+
+- `correction_reg_coef` 默认 0.03，设为 0 可禁用
+- correction 在 PPO 训练时从 stored actions 重新计算（与环境中的公式一致）
+- 目标：corr_std 不再从 ~0.03 持续涨到 ~0.15；r_le_sc 保持更接近 η baseline；validation aw_rel 不随训练后期变差
+- 训练 reward 可能因正则化而下降，这是正常现象；成功标准是测试误差更稳定
+
+### 训练诊断字段
+
+| 字段 | 来源 | 说明 |
+|------|------|------|
+| `corr_reg` | train_step | L_corr = coef × mean(corr²)，监控 correction drift |
+| `corr_l2` | train_step | mean(correction²)，correction 幅值 |
+| `corr_abs` | train_step | mean(\|correction\|)，correction 绝对值 |
+| `penalty_scale` | environment | step0=0.3，后续=1.0 |
+| `avg_penalty` | environment | 平均 element penalty（refined parents） |
+| `avg_r_local` | environment | 平均 r_local（penalty 前，refined parents） |
+| `step_id` | environment | 当前 timestep |
+
+---
+
+## 配置参考
+
+```yaml
+algorithm:
+ batch_size: 32
+ discount_factor: 1.0
+ ppo:
+ clip_range: 0.2
+ entropy_coefficient: 0.01
+ correction_reg_coef: 0.03 # correction 正则化系数
+ epochs_per_iteration: 3
+ gae_lambda: 0.95
+ initial_log_std: -2.0
+ max_grad_norm: 0.5
+ num_rollout_steps: 256
+ value_function_coefficient: 0.5
+ use_gpu: true
+
+environment:
+ mesh_refinement:
+ correction_scale: 0.3 # c in score = log(η) + c·tanh(δ)
+ step0_penalty_scale: 0.3 # step 0 element penalty 降权
+ num_timesteps: 4
+ refinement_strategy: continuous_sizing_field
+ reward_type: spatial
+ element_penalty:
+ value: 0.02
+ maximum_elements: 50000
+ element_limit_penalty: 10000
+ # ... (FEM / Helmholtz / 特征配置见 config.yaml)
+
+network:
+ latent_dimension: 64
+ use_global_conditioned_correction: true # Actor/Critic 拼接 g_global + 局部相对特征
+ use_global_stats: true # 启用 MultiPoolGVN + 13 维全局统计
+ gvn_pooling: [mean, eta_softmax] # 池化策略（可选加 top_eta）
+ correction_centering: true # correction 在 eligible 集内中心化
+ base:
+ edge_dropout: 0.1
+ scatter_reduce: mean
+ stack:
+ num_steps: 2
+ mlp:
+ activation_function: leakyrelu
+ num_layers: 2
+ actor:
+ mlp:
+ activation_function: tanh
+ num_layers: 2
+ critic:
+ mlp:
+ activation_function: tanh
+ num_layers: 2
+ training:
+ learning_rate: 0.0003
+ lr_decay: 1.0
+```
+
+### 实验对照建议
+
+| 实验 | `correction_reg_coef` | `step0_penalty_scale` | 目的 |
+|------|----------------------|----------------------|------|
+| A (baseline) | 0.0 | 1.0 | 无正则、无降权 |
+| B (corr reg only) | 0.03 | 1.0 | 验证 correction 正则效果（优先） |
+| C (both) | 0.03 | 0.3 | 正则 + step0 降权 |
+
+成功标准（非训练 reward 高低）：
+- `corr_std` 不再持续涨到 ~0.15
+- `r_le_sc` 保持更接近 η baseline
+- top-k overlap 不随训练后期明显下降
+- validation `aw_rel / max_err` 更稳定
+
+---
+
+## Correction GNN 训练数据
+
+Correction GNN 用于二分类预测：给定当前网格，哪些单元需要加密（teacher_mark=1）。
+训练数据由 `outlook/src/gen.py` 生成。
+
+### 参数采样
+
+每个样本随机采样物理参数：
+
+| 参数 | 分布 | 说明 |
+|------|------|------|
+| `k` | Uniform(3, 15) | 波数 |
+| `eps_r` | Uniform(2, 8) | 介质相对介电常数 |
+| `cx` | Uniform(0.2, 0.8) | 散射体中心 x |
+| `cy` | Uniform(0.2, 0.8) | 散射体中心 y |
+| `radius` | Uniform(0.05, 0.25) | 散射体半径 |
+
+### 初始网格
+
+采用物理自适应初始网格（`make_initial_mesh`），元素尺寸由局域波长决定：
+
+- **介质外**: h ≤ λ₀ / q, λ₀ = 2π / k
+- **介质内/散射体附近**: h ≤ λ_eff / q, λ_eff = 2π / (k √ε_r)
+- **q = 2**（每波长 2 个单元）
+
+网格在 [0,1]×[0,1] 域上通过张量积生成，x/y 方向各自根据散射体位置做分级加密：
+- 远离散射体：粗网格（h = λ₀/q）
+- 散射体附近（含过渡区）：细网格（h = λ_eff/q）
+
+### AMR 循环与标签生成
+
+对每个参数样本，运行残差驱动 AMR 循环，每步保存快照：
+
+```
+for step in range(max_steps):
+ 1. FEM 求解 → u_scat
+ 2. 计算残差指示子 η（teacher 信号）
+ 3. 计算 physics_score = h / λ_eff（物理 baseline）
+ 4. teacher_mark = top-fraction(η, mark_fraction) # 二值标签
+ physics_mark = top-fraction(physics_score, mark_fraction) # 物理 baseline
+ correction_label = teacher_mark - physics_mark # {-1, 0, +1}
+ 5. 提取 16 维节点特征 + 边索引
+ 6. 保存 .npz → 残差指示子 top-k 加密 → 下一步
+```
+
+- **mark_fraction**: 默认 0.03（每步标记 top 3% 的单元为正样本）
+- **top-fraction**: 按 score 降序取 top `n × fraction` 个单元，标记为 1
+- **teacher_mark**: 以 η（残差指示子）为 score，代表"最优加密目标"
+- **physics_mark**: 以 h/λ_eff 为 score，代表"纯物理 baseline"
+- **correction_label**: teacher 与 physics 的差集，+1 = teacher 独有（GNN 应补充），-1 = physics 独有（GNN 应抑制）
+
+### 数据文件格式
+
+每个样本每步保存为 `sample{id}_step{step}.npz`，包含：
+
+| 字段 | 形状 | 说明 |
+|------|------|------|
+| `features` | (n_elem, 16) | 15 维几何/PDE 特征 + 1 维 physics_score |
+| `edge_index` | (2, n_edges) | 双向边 + 自环 |
+| `physics_score` | (n_elem,) | h / λ_eff |
+| `teacher_eta` | (n_elem,) | 残差指示子 η |
+| `teacher_mark` | (n_elem,) | 二值标签 (0/1) |
+| `physics_mark` | (n_elem,) | 物理 baseline 标签 (0/1) |
+| `correction_label` | (n_elem,) | 差集标签 (-1/0/+1) |
+| `k, eps_r, cx, cy, radius` | scalar | 物理参数 |
+| `elements` | scalar | 当前单元数 |
+| `step` | scalar | AMR 步数 |
+
+---
+
+## One-Shot Density Prediction
+
+One-shot final mesh density prediction experiments are documented in [`outlook/README.md`](outlook/README.md).
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--- a/environment/mesh_refinement.py
+++ b/environment/mesh_refinement.py
@@ -1,3 +1,4 @@
+import time
from typing import Any, Callable, Dict, List, Optional, Tuple, Union
import gym
@@ -55,7 +56,6 @@ class MeshRefinement(gym.Env):
# graph connectivity, feature and action space #
################################################
self._reward_type = environment_config.get("reward_type")
- self._global_reward_alpha = float(environment_config.get("global_reward_alpha", 0.2))
_rho_w = environment_config.get("rho_weights", {})
self._w_rho_int = float(_rho_w.get("w_int", 1.0))
self._w_rho_jump = float(_rho_w.get("w_jump", 1.0))
@@ -223,6 +223,25 @@ class MeshRefinement(gym.Env):
self._diag_selected_count = -1 # 防止跨 episode 残留触发 is_terminal
self._diag_dorfler_tail_ratio = 0.0
self._diag_dorfler_floor_active = False
+ self._diag_corr_raw_mean = 0.0
+ self._diag_corr_mean = 0.0
+ self._diag_corr_std = 0.0
+ self._diag_corr_abs = 0.0
+ self._diag_neg_ratio = 0.0
+ self._diag_score_eta_corr = 0.0
+ self._diag_max_by_budget = 0
+ self._diag_max_by_growth = 0
+ self._diag_n_budget = 0
+ self._diag_remaining = 0
+ self._diag_n_eligible = 0
+ self._diag_n_next = 0
+ self._diag_corr_rel_eta_corr = 0.0
+ self._diag_corr_inside_mean = 0.0
+ self._diag_corr_outside_mean = 0.0
+ self._diag_corr_top_eta_mean = 0.0
+ self._diag_corr_low_eta_mean = 0.0
+ self._diag_global_top10_eta_energy = 0.0
+ self._diag_remaining_ratio = 0.0
# reset internal state that tracks statistics over the episode
self._previous_error_per_element = self.error_per_element
@@ -325,9 +344,11 @@ class MeshRefinement(gym.Env):
# solve equation and calculate error per element/element
self._previous_error_per_element = self.error_per_element
+ t_fem = time.perf_counter()
self._error_estimation_dict = (
self.fem_problem.calculate_solution_and_get_error()
)
+ self._last_fem_solve_ms = (time.perf_counter() - t_fem) * 1e3
# query returns
observation = self.last_observation
@@ -346,12 +367,30 @@ class MeshRefinement(gym.Env):
"is_truncated": self.is_truncated,
"return": self._cumulative_return,
"neg_action_ratio": getattr(self, "_diag_neg_ratio", 0.0),
+ "corr_raw_mean": getattr(self, "_diag_corr_raw_mean", 0.0),
+ "corr_mean": getattr(self, "_diag_corr_mean", 0.0),
+ "corr_std": getattr(self, "_diag_corr_std", 0.0),
+ "corr_abs": getattr(self, "_diag_corr_abs", 0.0),
+ "score_eta_corr": getattr(self, "_diag_score_eta_corr", 0.0),
"eligible_ratio": getattr(self, "_diag_eligible_ratio", 0.0),
"masked_ratio": getattr(self, "_diag_masked_ratio", 0.0),
"selected_count": getattr(self, "_diag_selected_count", 0),
"dorfler_tail_ratio": getattr(self, "_diag_dorfler_tail_ratio", 0.0),
"dorfler_floor_active": float(getattr(self, "_diag_dorfler_floor_active", False)),
"n_budget": self._n_budget,
+ "remaining": getattr(self, "_diag_remaining", 0),
+ "max_by_budget": getattr(self, "_diag_max_by_budget", 0),
+ "max_by_growth": getattr(self, "_diag_max_by_growth", 0),
+ "n_eligible": getattr(self, "_diag_n_eligible", 0),
+ "n_next": getattr(self, "_diag_n_next", 0),
+ "fem_solve_ms": self._last_fem_solve_ms,
+ "corr_rel_eta_corr": getattr(self, "_diag_corr_rel_eta_corr", 0.0),
+ "corr_inside_mean": getattr(self, "_diag_corr_inside_mean", 0.0),
+ "corr_outside_mean": getattr(self, "_diag_corr_outside_mean", 0.0),
+ "corr_top_eta_mean": getattr(self, "_diag_corr_top_eta_mean", 0.0),
+ "corr_low_eta_mean": getattr(self, "_diag_corr_low_eta_mean", 0.0),
+ "global_top10_eta_energy": getattr(self, "_diag_global_top10_eta_energy", 0.0),
+ "remaining_ratio": getattr(self, "_diag_remaining_ratio", 0.0),
}
)
return observation, self._reward, done, info
@@ -527,31 +566,56 @@ class MeshRefinement(gym.Env):
if self._refinement_strategy == "continuous_sizing_field":
# ================================================================
- # Score-based 细化选择（由 actor 直接排序，物理预算约束）
+ # Score-based 细化选择：log(η) baseline + bounded Actor correction
#
- # Actor 输出标量 x_i: x_i < 0 → 希望细化; x_i > 0 → 不希望细化
- # 排序依据 score = -x_i，在预算和上限内选 top-k
+ # score_i = log(η_i + eps) + c · tanh(δ_i)
#
- # 物理预算 N_budget: Σ area_K / A_budget，其中
- # A_budget = ½(λ_local/6)²，对应每局部波长方向 ~6 个尺度点
+ # η_i = current-step residual indicator (physical prior)
+ # δ_i = Actor output (continuous scalar per element)
+ # c = correction_scale (0.7) — bounds Actor influence
+ # eps = dynamic: 0.01 · median(η) — prevents log(0)
#
- # 动作掩码 (Reverse Dörfler): 按 η_K 升序排列，剔除累积平方误差
- # 贡献 < ε_noise·Ση² 的底部单元（数值噪声/已收敛区），保留 ≥20%
- # 的单元确保 Agent 始终有充分的选择空间
+ # Selection: top-k by score descending (higher score → refine).
+ # Actor can boost or suppress priority by at most ±c in the log-η
+ # domain, but cannot override the physical prior.
# ================================================================
- x = action.flatten()
+ delta = action.flatten()
- # ── 训练监控指标（在所有 early return 之前计算）──
- self._diag_neg_ratio = float(np.mean(x < 0.0))
+ eta = self._eta_indicator
+ eps_score = max(0.01 * float(np.median(eta)), 1e-12)
+ log_eta = np.log(np.maximum(eta, 1e-30) + eps_score)
+
+ c = float(self._environment_config.get("correction_scale", 0.7))
+ corr_raw = c * np.tanh(delta)
remaining = self._n_budget - self._num_elements
- max_parents_by_budget = max(0, remaining // 3)
+ max_parents_by_budget = max(0, remaining // 6)
+
+ self._diag_max_by_budget = max_parents_by_budget
if max_parents_by_budget <= 0:
self._diag_eligible_ratio = 0.0
self._diag_selected_count = 0
self._diag_dorfler_tail_ratio = 0.0
self._diag_dorfler_floor_active = False
+ self._diag_max_by_growth = max(1, self._num_elements // 4)
+ self._diag_n_budget = self._n_budget
+ self._diag_remaining = remaining
+ self._diag_n_eligible = 0
+ self._diag_n_next = self._num_elements
+ self._diag_corr_raw_mean = float(np.mean(corr_raw))
+ self._diag_corr_mean = 0.0
+ self._diag_corr_std = 0.0
+ self._diag_corr_abs = 0.0
+ self._diag_neg_ratio = float(np.mean(delta < 0.0))
+ self._diag_score_eta_corr = 0.0
+ self._diag_corr_rel_eta_corr = 0.0
+ self._diag_corr_inside_mean = 0.0
+ self._diag_corr_outside_mean = 0.0
+ self._diag_corr_top_eta_mean = 0.0
+ self._diag_corr_low_eta_mean = 0.0
+ self._diag_global_top10_eta_energy = 0.0
+ self._diag_remaining_ratio = remaining / max(self._n_budget, 1)
return np.array([], dtype=np.int64)
# 动态计算每单元预算面积（仅用于 N_budget 全局资源上限）
@@ -560,32 +624,23 @@ class MeshRefinement(gym.Env):
lambda_local = 2.0 * np.pi / (k * np.sqrt(np.maximum(eps_r_elem, 1.0)))
A_budget = 0.5 * (lambda_local / 6.0) ** 2
- # 纯数值安全底线：仅防止 scikit-fem 因浮点精度导致的退化/奇异。
- # 不再用 0.25*A_budget —— RL 应自主学会"多细才够"，
- # 而非被人为启发式 (12 点/波长) 限制。
domain_area = float(np.prod(self.fem_problem.plot_boundary[2:] - self.fem_problem.plot_boundary[:2]))
V_min_safeguard = 1e-10 * domain_area
- # Filter 1: numerical safeguard only — no physics heuristic
+ # Filter 1: numerical safeguard only
area_eligible = np.where(self.element_volumes > V_min_safeguard)[0]
- # Filter 2: Reverse Dörfler — eliminate the noise tail, not select the elite.
- # Sort η_K ascending; remove the smallest elements whose cumulative η²
- # contributes < ε_noise of total error energy. These are numerically
- # converged or noise — not worth the agent's attention.
- # A 20% floor on the eligible ratio guarantees the agent meaningful
- # choices even in heavy-tailed distributions where energy is concentrated.
+ # Filter 2: Reverse Dörfler — eliminate noise tail
eta_current = self._eta_indicator
eta_sq = eta_current ** 2
total_energy = np.sum(eta_sq)
if total_energy > 0:
- idx_asc = np.argsort(eta_current) # ascending
+ idx_asc = np.argsort(eta_current)
cumsum_asc = np.cumsum(eta_sq[idx_asc])
- eps_noise = 0.01 # bottom 1% of energy = noise tail
+ eps_noise = 0.01
k_dorfler = int(np.searchsorted(cumsum_asc, eps_noise * total_energy))
self._diag_dorfler_tail_ratio = float(k_dorfler) / max(self._num_elements, 1)
- # floor: keep at least 20% of elements for RL agent choice
min_keep = max(1, self._num_elements // 5)
k = min(k_dorfler, self._num_elements - min_keep)
self._diag_dorfler_floor_active = k < k_dorfler
@@ -597,26 +652,104 @@ class MeshRefinement(gym.Env):
eligible = np.intersect1d(area_eligible, error_eligible)
+ # ── correction centering (eligible only) ──
+ # Global shift is meaningless for top-k ranking; center within
+ # eligible candidates so the Actor only controls relative priority.
+ self._diag_corr_raw_mean = float(np.mean(corr_raw))
+ if len(eligible) > 0:
+ corr = corr_raw - np.mean(corr_raw[eligible])
+ else:
+ corr = corr_raw - np.mean(corr_raw)
+
+ score = log_eta + corr
+
+ # ── diagnostics ──
+ self._diag_neg_ratio = float(np.mean(delta < 0.0))
+ self._diag_corr_mean = float(np.mean(corr))
+ self._diag_corr_std = float(np.std(corr))
+ self._diag_corr_abs = float(np.mean(np.abs(corr)))
+ # Spearman-like: Pearson r between log_eta and score
+ le = log_eta - log_eta.mean()
+ sc = score - score.mean()
+ denom = np.sqrt(np.sum(le**2) * np.sum(sc**2))
+ self._diag_score_eta_corr = float(np.sum(le * sc) / max(denom, 1e-12))
+
self._diag_eligible_ratio = float(len(eligible)) / max(self._num_elements, 1)
self._diag_masked_ratio = (
1.0 - float(len(eligible)) / max(len(area_eligible), 1)
if len(area_eligible) > 0 else 0.0
)
+ # ── GVN global-conditioned correction diagnostics ──
+ # corr-rel_logeta correlation
+ rel_le = log_eta - log_eta.mean()
+ rel_corr = corr - corr.mean()
+ denom_rc = np.sqrt(np.sum(rel_le**2) * np.sum(rel_corr**2))
+ self._diag_corr_rel_eta_corr = float(
+ np.sum(rel_le * rel_corr) / max(denom_rc, 1e-12)
+ )
+
+ # correction by region (inside/outside scatterer)
+ eps_r = self._epsilon_r_elements
+ inside_mask = eps_r > 1.0
+ outside_mask = ~inside_mask
+ self._diag_corr_inside_mean = float(np.mean(corr[inside_mask])) if inside_mask.any() else 0.0
+ self._diag_corr_outside_mean = float(np.mean(corr[outside_mask])) if outside_mask.any() else 0.0
+
+ # correction by eta rank
+ eta = self._eta_indicator
+ k10 = max(1, int(0.1 * self._num_elements))
+ top_idx = np.argsort(eta)[-k10:]
+ low_idx = np.argsort(eta)[:self._num_elements // 2]
+ self._diag_corr_top_eta_mean = float(np.mean(corr[top_idx]))
+ self._diag_corr_low_eta_mean = float(np.mean(corr[low_idx]))
+
+ # global top10 eta energy and remaining ratio
+ eta_sq = eta ** 2
+ total_energy = float(np.sum(eta_sq))
+ self._diag_global_top10_eta_energy = (
+ float(np.sum(eta_sq[top_idx])) / (total_energy + 1e-12)
+ )
+ self._diag_remaining_ratio = remaining / max(self._n_budget, 1)
+
+ max_by_growth = max(1, self._num_elements // 4)
+ self._diag_max_by_growth = max_by_growth
+ self._diag_n_budget = self._n_budget
+ self._diag_remaining = remaining
+ self._diag_n_eligible = len(eligible)
+
num = min(
len(eligible),
- max(1, self._num_elements // 4),
+ max_by_growth,
max_parents_by_budget,
)
if num <= 0:
self._diag_selected_count = 0
+ self._diag_n_next = self._num_elements
return np.array([], dtype=np.int64)
- # x 越小 ⇒ 优先级越高（纯排序，不设正负门槛）
- score = -x
- selected = eligible[np.argsort(score[eligible])[-num:]]
+ # top-k by score descending with physical tie-breaking
+ # (avoids spatially arbitrary selection when scores are tied)
+ _fp = self.fem_problem.fem_problem
+ _cx = getattr(_fp, "_cx", 0.5)
+ _cy = getattr(_fp, "_cy", 0.5)
+ _radius = getattr(_fp, "_radius", 0.2)
+ _mesh = self.mesh
+ _p = _mesh.p
+ _t = _mesh.t
+ _mx = (_p[0, _t[0]] + _p[0, _t[1]] + _p[0, _t[2]]) / 3.0
+ _my = (_p[1, _t[0]] + _p[1, _t[1]] + _p[1, _t[2]]) / 3.0
+ _dist = np.sqrt((_mx - _cx)**2 + (_my - _cy)**2)
+ _sd = _dist - _radius
+ _inside = (_dist <= _radius).astype(np.float32)
+ _abs_sd = np.abs(_sd[eligible])
+ _inside_elig = _inside[eligible]
+ _tie_key = -_abs_sd + _inside_elig
+ _composite = score[eligible] * 1e6 + _tie_key
+ selected = eligible[np.argsort(_composite)[-num:]]
self._diag_selected_count = len(selected)
+ self._diag_n_next = self._num_elements + len(selected) * 3 # estimate
elements_to_refine = selected
elif self._refinement_strategy in ["absolute", "absolute_discrete"]:
@@ -700,6 +833,93 @@ class MeshRefinement(gym.Env):
error_per_dim = np.sqrt(np.sum(error_per_element**2, axis=0))
return float(self.project_to_scalar(error_per_dim))
+ @property
+ def num_global_stats(self) -> int:
+ """Number of global statistics attached to each graph observation."""
+ return 13
+
+ def _compute_global_stats(self) -> np.ndarray:
+ """Compute graph-level global statistics for GVN conditioning.
+
+ Returns: np.ndarray of shape (num_global_stats,) with keys:
+ [0] remaining_ratio — (N_budget - N_current) / N_budget
+ [1] step_ratio — current_step / max_steps
+ [2] elem_ratio — N_current / N_budget
+ [3] logeta_mean
+ [4] logeta_std
+ [5] logeta_max
+ [6] logeta_p90
+ [7] logeta_p75
+ [8] top10_eta_energy_ratio — top 10% eta^2 energy / total
+ [9] eligible_ratio — elements above area safeguard / total
+ [10] inside_eta_energy — eta energy inside scatterer / total
+ [11] outside_eta_energy — eta energy outside scatterer / total
+ [12] interface_eta_energy — eta energy near interface / total
+ """
+ eta = self._eta_indicator
+ N = self._num_elements
+ eps = 1e-12
+
+ # log-eta for percentile stats
+ eps_score = max(0.01 * float(np.median(eta)), 1e-12)
+ logeta = np.log(np.maximum(eta, 1e-30) + eps_score)
+
+ # budget stats
+ remaining = max(0, self._n_budget - N)
+ remaining_ratio = remaining / max(self._n_budget, 1)
+ step_ratio = self._timestep / max(self._max_timesteps, 1)
+ elem_ratio = N / max(self._n_budget, 1)
+
+ # logeta stats
+ le_mean = float(np.mean(logeta))
+ le_std = float(np.std(logeta)) + 1e-8
+ le_max = float(np.max(logeta))
+ le_p90 = float(np.percentile(logeta, 90))
+ le_p75 = float(np.percentile(logeta, 75))
+
+ # top 10% eta energy ratio
+ eta_sq = eta ** 2
+ total_energy = float(np.sum(eta_sq))
+ if total_energy > 0:
+ k10 = max(1, int(0.1 * N))
+ top10_idx = np.argsort(eta_sq)[-k10:]
+ top10_ratio = float(np.sum(eta_sq[top10_idx])) / (total_energy + eps)
+ else:
+ top10_ratio = 0.0
+
+ # eligible ratio (area safeguard)
+ domain_area = float(np.prod(
+ self.fem_problem.plot_boundary[2:] - self.fem_problem.plot_boundary[:2]
+ ))
+ V_min = 1e-10 * domain_area
+ eligible_ratio = float(np.sum(self.element_volumes > V_min)) / max(N, 1)
+
+ # region eta energy ratios
+ eps_r = self._epsilon_r_elements
+ inside_mask = eps_r > 1.0
+ outside_mask = ~inside_mask
+
+ fp = self.fem_problem.fem_problem
+ cx = getattr(fp, "_cx", 0.5)
+ cy = getattr(fp, "_cy", 0.5)
+ radius = getattr(fp, "_radius", 0.2)
+ midpoints = self._element_midpoints
+ dist_raw = np.sqrt((midpoints[:, 0] - cx)**2 + (midpoints[:, 1] - cy)**2)
+ lam = 2.0 * np.pi / max(self._wave_number, 1e-8)
+ interface_mask = np.abs(dist_raw - radius) < 0.2 * lam
+
+ inside_energy = float(np.sum(eta_sq[inside_mask])) / (total_energy + eps)
+ outside_energy = float(np.sum(eta_sq[outside_mask])) / (total_energy + eps)
+ interface_energy = float(np.sum(eta_sq[interface_mask])) / (total_energy + eps)
+
+ stats = np.array([
+ remaining_ratio, step_ratio, elem_ratio,
+ le_mean, le_std, le_max, le_p90, le_p75,
+ top10_ratio, eligible_ratio,
+ inside_energy, outside_energy, interface_energy,
+ ], dtype=np.float32)
+ return stats
+
@property
def last_observation(self) -> Data:
"""
@@ -716,6 +936,10 @@ class MeshRefinement(gym.Env):
observation_graph = Data(**graph_dict)
observation_graph.eta = torch.tensor(self._eta_indicator, dtype=torch.float32)
+ observation_graph.area = torch.tensor(self.element_volumes, dtype=torch.float32)
+ observation_graph.global_stats = torch.tensor(
+ self._compute_global_stats(), dtype=torch.float32
+ ).unsqueeze(0) # [1, num_global_stats]
return observation_graph
@@ -932,25 +1156,16 @@ class MeshRefinement(gym.Env):
reward_per_agent = self.project_to_scalar(reward_per_agent_and_dim)
- # ── Causal isolation + bounded signals ──
- # r_local: clipped to [−1, +1] — prevents pollution-error inversions
- # (±4.6) from hijacking the Critic's value estimate.
- # r_bonus: 0.5·tanh(η/μ − 1) — linear near μ (preserves Dörfler),
- # saturates at ±0.5 for extreme η, bounded and safe.
- # Unrefined parents: r = 0 (causal isolation).
+ # ── Pure local improvement reward (no modulation, no bonus) ──
+ # r_i = clip(log(η_old) − log(l2(η_child)), 0, rmax)
+ # L₂ aggregation guarantees r_local ≥ 0; clip lower bound at 0 as
+ # a safety floor against floating-point noise.
+ rmax = 2.0
unique_old, counts = np.unique(self.agent_mapping, return_counts=True)
refined_mask = np.zeros(len(reward_per_agent), dtype=bool)
refined_mask[unique_old[counts > 1]] = True
- # Clip r_local to prevent outlier-driven value collapse
- reward_per_agent = np.clip(reward_per_agent, -1.0, 1.0)
-
- # Bounded state bonus: tanh preserves Dörfler near μ, caps at extreme η
- eta_raw = self._previous_eta_indicator
- mu_eta = float(np.mean(eta_raw))
- reward_per_agent[refined_mask] += 0.5 * np.tanh(
- eta_raw[refined_mask] / (mu_eta + 1e-8) - 1.0
- )
+ reward_per_agent = np.clip(reward_per_agent, 0.0, rmax)
# Unrefined: clean zero (causal isolation)
reward_per_agent[~refined_mask] = 0.0
@@ -958,31 +1173,30 @@ class MeshRefinement(gym.Env):
# apply action/element penalty (refined parents only)
element_penalty = np.zeros(len(reward_per_agent), dtype=reward_per_agent.dtype)
element_penalty[unique_old] = self._element_penalty_lambda * (counts - 1)
+
+ # Step 0 penalty scaling: reduce element penalty on first refinement step
+ # to prevent "reward < 0 but aw_rel improved" feedback inversion.
+ step0_scale = float(self._environment_config.get("step0_penalty_scale", 1.0))
+ penalty_scale = step0_scale if self._timestep == 1 else 1.0
+ element_penalty = element_penalty * penalty_scale
+
element_limit_penalty = (
(self._element_limit_penalty / self._previous_num_elements)
if self.reached_element_limits
else 0
)
+
+ # Step 0 diagnostics (r_local = reward before penalty, already clipped)
+ r_local_pre_penalty = reward_per_agent.copy()
+ _step0_penalty_scale = penalty_scale
+ _step0_avg_penalty = float(np.mean(element_penalty[refined_mask])) if refined_mask.any() else 0.0
+ _step0_avg_r_local = float(np.mean(r_local_pre_penalty[refined_mask])) if refined_mask.any() else 0.0
+ _step0_step_id = self._timestep
+
reward_per_agent = (
reward_per_agent - element_penalty - element_limit_penalty
)
- # ── Global error change (diagnostic only, NOT injected into Actor reward) ──
- # Removing global_bonus from per-element reward eliminates the broken causal
- # chain: Helmholtz pollution error can make E_new > E_old even when the
- # selected elements were the right choice, punishing agents for physics
- # they didn't cause. Actor optimises r_local only; Critic captures global
- # effects through value estimation.
- l2_old = self._previous_solution_l2_norm
- l2_new = self._compute_solution_l2_norm()
- eta_l2_old = float(np.sqrt(np.sum(old_eta ** 2)))
- eta_l2_new = float(np.sqrt(np.sum(new_eta ** 2)))
- eps_l2 = 1e-12
- E_old = eta_l2_old / max(l2_old, eps_l2)
- E_new = eta_l2_new / max(l2_new, eps_l2)
- global_bonus = self._global_reward_alpha * float(np.log(E_old + eps_l2) - np.log(E_new + eps_l2))
- # global_bonus intentionally NOT added to reward_per_agent — see above.
-
self._reward_per_agent = reward_per_agent
self._cumulative_reward_per_agent = (
self._cumulative_reward_per_agent[self._previous_agent_mapping]
@@ -991,11 +1205,15 @@ class MeshRefinement(gym.Env):
reward = reward_per_agent
reward_dict["reward"] = reward
- reward_dict["potential_bonus"] = global_bonus
reward_dict["penalty"] = -reward
reward_dict["element_limit_penalty"] = element_limit_penalty
reward_dict["element_penalty"] = element_penalty
reward_dict["element_penalty_lambda"] = self._element_penalty_lambda
+ # Step 0 penalty scaling diagnostics
+ reward_dict["penalty_scale"] = _step0_penalty_scale
+ reward_dict["avg_penalty"] = _step0_avg_penalty
+ reward_dict["avg_r_local"] = _step0_avg_r_local
+ reward_dict["step_id"] = _step0_step_id
return reward, reward_dict
@property
diff --git a/outlook/README.md b/outlook/README.md
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+# Outlook: GNN-Guided Adaptive Mesh Refinement for 2D Helmholtz Scattering
+
+## 1. 问题定义
+
+求解 2D 介质圆柱的电磁散射（散射场公式）：
+
+```
+∇²u + k²·ε_r·u = −k²·(ε_r − 1)·u_inc
+∂u/∂n − i·k_local·u = 0 (Sommerfeld 辐射 BC)
+```
+
+- 入射波：`u_inc = exp(i·k·x)`，参考解：Mie 解析解
+- 参数空间：k∈[3,15]，eps_r∈[2,8]，cx/cy∈[0.2,0.8]，radius∈[0.05,0.25]
+- 核心目标：在参数化 Helmholtz 散射问题中，学习一个无在线求解的预算约束网格预测器，用于近似 residual-AMR 的最终加密分布，并在低预算下优于简单物理启发式网格。
+
+---
+
+## 2. 算法全流程
+
+```
+Step 1. 数据生成 (gen.py)
+ 残差驱动 AMR → 每步保存 cell 状态 + 标签
+ │
+ ▼
+Step 2. 训练 (train_correction.py)
+ features(15-dim) + physics_score → GNN → sigmoid → 二分类 teacher_mark
+ │
+ ▼
+Step 3. 评估
+ 3a. 离线指标 (test_correction.py) — top-k overlap / AUC
+ 3b. Rollout 评估 (eval_correction.py) — 迭代加密 → FEM → aw_rel
+ │
+ ▼
+Step 4. 可视化 (viz_correction.py)
+ amr 模式: GNN 驱动完整 AMR → 网格 + 场 + 误差
+ step 模式: 单步 GNN vs teacher vs physics 标记对比
+```
+
+---
+
+## 3. 数据生成 (`gen.py`)
+
+### 3.1 初始网格
+
+物理自适应初始网格（`build_physics_safe_initial_mesh`）：
+
+- 均匀基底网格 + 迭代局部加密
+- 介质外：h ≤ λ₀/q，介质内：h ≤ λ_eff/q（q=2，每波长 2 个单元）
+- 加密准则：`score = max_edge / h_target > 1` 的单元被加密
+- 二分搜索控制每批加密数量，不超预算
+
+### 3.2 AMR 循环（每步保存）
+
+```
+初始 mesh → FEM solve → 残差估计器 η → teacher_mark (η top-k)
+ ├── physics_score → physics_mark (top-k)
+ ├── correction_label = teacher_mark − physics_mark
+ └── 保存 .npz → 按 η 选单元加密 → 下一步
+```
+
+**残差估计器 η**（`environment/helmholtz.py:_compute_residual_indicator`）：
+- 内部残差：`h_K/k · √V_K · |k²ε_r·u_h + k²(ε_r−1)·u_inc|`
+- 梯度跳变：`√(½ Σ h_e/k · |[[∇u_h·n]]|²)`
+- SBC 边界残差：`h_bnd/k · |∂u/∂n − i·k_local·u|`
+
+**标记策略**：
+- teacher_mark：按 η 取 top `mark_fraction`（默认 3%）
+- physics_mark：按 `physics_score` 取 top `mark_fraction`
+- correction_label = +1（teacher 独有）、0（一致）、−1（physics 独有）
+
+**安全过滤**：
+1. 面积过滤：排除面积 ≤ 1e-10 的退化单元
+2. 反向 Dörfler：排除误差贡献最低 1% 的单元
+
+### 3.3 输出格式
+
+```
+outlook/data_correction/
+├── params_list.npz # (n_samples, 5) PDE 参数
+├── sample0000_step000.npz # 逐样本逐步数据
+└── summary.json
+```
+
+每个 step .npz：
+
+| 字段 | 形状 | 说明 |
+|------|------|------|
+| `features` | `(n_elem, 15)` | 几何/物理特征 |
+| `edge_index` | `(2, n_edges)` | 网格图结构 |
+| `physics_score` | `(n_elem,)` | h/λ_eff |
+| `teacher_eta` | `(n_elem,)` | 残差估计器 |
+| `teacher_mark` | `(n_elem,)` | η top-k 标记 (0/1) |
+| `physics_mark` | `(n_elem,)` | physics top-k 标记 (0/1) |
+| `correction_label` | `(n_elem,)` | teacher − physics (−1/0/+1) |
+
+---
+
+## 4. 特征工程
+
+### 4.1 15 维基础特征
+
+| 维 | 特征 | 说明 |
+|----|------|------|
+| 0,1 | x, y | 单元中点坐标 |
+| 2 | area | 单元面积 |
+| 3 | dist_to_center | 到圆柱中心距离 |
+| 4 | signed_dist | dist − radius（负=介质内） |
+| 5 | inside | 是否在圆柱内 (0/1) |
+| 6 | k | 波数 |
+| 7 | eps_r | 介电常数 |
+| 8 | radius | 半径 |
+| 9,10 | cx, cy | 圆柱中心 |
+| 11 | k_h | k × √area |
+| 12 | k_eps_h | k × √eps_r × √area |
+| 13,14 | sin(k·x), cos(k·x) | 入射波相位 |
+
+### 4.2 Physics Score（第 16 维输入）
+
+```python
+lambda_eff = 2π / (k · √eps_r) # 介质内
+ 或 2π / k # 介质外
+physics_score = max_edge / lambda_eff # >1 = 分辨率不足
+```
+
+### 4.3 归一化
+
+训练集 z-score 归一化，推理复用同一统计量：
+```python
+x_norm = (concat(features, physics_score) - mean) / scale
+```
+
+---
+
+## 5. GNN 架构
+
+### 5.1 CorrectionGNN
+
+基于 DensityGNN 骨干，替换密度回归头为二分类 logit 头：
+
+```
+Input: (n_cells, 16) node features
+ │
+ ├── node_embedding: Linear(16 → latent_dim)
+ ├── edge_embedding: Linear(16 → latent_dim)
+ │
+ ├── N × MessagePassingStep:
+ │ ├── EdgeModule: MLP([src | dst | edge_attr]) → latent_dim
+ │ ├── NodeModule: MLP([node | mean(incoming_edges)]) → latent_dim
+ │ └── LayerNorm + Residual
+ │
+ ├── GlobalVirtualNode: mean_pool → attention_gate → broadcast
+ │
+ └── head: Linear(latent → hidden) → ReLU → Linear(hidden → 1 logit)
+```
+
+### 5.2 关键设计
+
+- 边特征：`edge_attr = |x[src] - x[dst]|`（节点特征差绝对值）
+- 边丢弃：训练 0.1，推理 0.0
+- 损失：BCEWithLogitsLoss + per-graph `pos_weight = neg/pos`
+
+### 5.3 训练配置
+
+| 参数 | 值 |
+|------|-----|
+| latent_dim | 64 |
+| num_mp_steps | 3 |
+| head_hidden | 64 |
+| lr | 1e-3 |
+| optimizer | Adam |
+| scheduler | ReduceLROnPlateau (patience=10) |
+
+---
+
+## 6. 评估体系
+
+### 6.1 离线指标（test_correction.py）
+
+- **top-k overlap**：GNN 概率最高的 k 个 cell 与 teacher_mark 的交集 / k
+- **AUC**：ROC-AUC（GNN vs physics baseline）
+- **gnn_beats_physics_ratio**：GNN 优于 physics 的样本比例
+
+### 6.2 Rollout 评估（eval_correction.py）
+
+从初始 mesh 出发，**无 teacher_eta，无残差标记，无中间 FEM solve**。每步只用分数决定加密单元，最终一次 FEM solve 计算误差。
+
+三种方法：
+
+| 方法 | 打分 | 说明 |
+|------|------|------|
+| `physics` | `physics_score` | 纯物理先验 |
+| `neural` | `model(features + physics_score)` | 纯 GNN |
+| `hybrid` | `α·zscore(physics) + β·zscore(neural)` | 混合（默认 α=β=0.5） |
+
+### 6.3 误差指标
+
+**aw_rel**（面积加权相对误差）：
+```
+aw_rel = √( Σ err²_tri · area / Σ ref²_tri · area )
+```
+
+**max_err**（最大逐点误差）：
+```
+max_err = max |Re(u_fem) − Re(u_mie)|
+```
+
+---
+
+## 7. 可视化
+
+### 7.1 amr 模式
+
+GNN 驱动完整 AMR，每步 FEM solve，展示网格和场演变。
+
+输出：
+- `amr_overview.png` — 所有步骤总览
+- `amr_steps/step{XX}.png` — 每步 3 面板（FEM 场 / Mie 参考 / 误差）
+- `ground_truth.png` — 高保真参考解（`--compare` 时）
+- `compare.png` — Physics vs GNN vs Eta 对比（`--compare` 时）
+
+### 7.2 step 模式
+
+重建指定 AMR 步的 mesh，对比 GNN / teacher / physics 标记。
+
+输出：
+- `marks_*.png` — 2×2 对比图（teacher / GNN / physics / TP/FP/FN/TN）
+- `field_gnn_*.png` — GNN 加密后 3 面板图
+- `field_eta_*.png` — 传统 η 加密后 3 面板图
+
+---
+
+## 8. 使用方法
+
+### 8.1 数据生成
+
+```bash
+python outlook/src/gen.py \
+ --n-samples 100 \
+ --max-elements 12000 \
+ --mark-fraction 0.03 \
+ --output-dir outlook/data_correction
+```
+
+### 8.2 训练
+
+```bash
+python outlook/src/train_correction.py \
+ --data-dir outlook/data_correction \
+ --epochs 100 \
+ --batch-size 32 \
+ --lr 1e-3 \
+ --device cuda \
+ --checkpoint-out outlook/ckpt/correction.pt
+```
+
+输出：
+- `correction.pt` — 最终模型
+- `correction_best.pt` — val_loss 最低 checkpoint
+- `correction_train_log.json` — 逐 epoch 日志
+
+### 8.3 离线指标评估
+
+```bash
+python outlook/src/test_correction.py \
+ --checkpoint outlook/ckpt/correction.pt \
+ --data-dir outlook/data_correction \
+ --device cuda \
+ --visualize \
+ --output-dir outlook/result/correction/test
+```
+
+### 8.4 Rollout 评估
+
+```bash
+python outlook/src/eval_correction.py \
+ --checkpoint outlook/ckpt/correction.pt \
+ --data-dir outlook/data_correction \
+ --target-elements 2000,4000,8000,12000 \
+ --mark-fraction 0.03 \
+ --max-steps 40 \
+ --methods physics,neural,hybrid \
+ --alpha 0.5 --beta 0.5 \
+ --device cuda \
+ --output-dir outlook/result/correction/rollout
+```
+
+输出：
+- `eval_results.json` — 详细结果 + 聚合统计 + 改善比例
+- `summary.csv` — 每行一个 (method, target) 汇总
+- `aw_rel_vs_elements.png` / `max_err_vs_elements.png`
+
+### 8.5 可视化
+
+```bash
+# 端到端 AMR
+python outlook/src/viz_correction.py \
+ --checkpoint outlook/ckpt/correction.pt \
+ --data-dir outlook/data_correction \
+ --mode amr --sample-id 0 --max-elements 5000 \
+ --device cuda \
+ --output-dir outlook/result/correction/viz
+
+# 单步对比
+python outlook/src/viz_correction.py \
+ --checkpoint outlook/ckpt/correction.pt \
+ --data-dir outlook/data_correction \
+ --mode step --sample-id 0 --step 0 \
+ --device cuda \
+ --output-dir outlook/result/correction/viz
+
+# OOD 评估（自定义物理参数，需同时指定 k, eps-r, cx, cy, radius）
+python outlook/src/viz_correction.py \
+ --checkpoint outlook/ckpt/correction.pt \
+ --data-dir outlook/data_correction \
+ --mode amr \
+ --k 30 --eps-r 4 --cx 0.5 --cy 0.5 --radius 0.15 \
+ --max-elements 6000 --compare \
+ --device cuda \
+ --output-dir outlook/result/correction/viz
+```
+
+---
+
+## 9. 目录结构
+
+```
+outlook/
+├── README.md # 本文档
+├── train.sh # SLURM 训练脚本（可配置 batch_size，默认 1）
+├── analyze_budget_teacher.py # Budget teacher 数据集分析
+├── check_correction_data.py # 数据质量校验
+│
+├── src/
+│ ├── gen.py # 数据生成
+│ ├── train_correction.py # 训练
+│ ├── test_correction.py # 离线指标评估
+│ ├── eval_correction.py # Rollout 评估
+│ ├── viz_correction.py # 可视化
+│ ├── rollout.py # 统一 AMR rollout（核心循环 + 共享 refinement 工具）
+│ ├── gnn.py # DensityGNN 模型
+│ ├── feat.py # 特征提取
+│ ├── graph.py # mesh → PyG graph（含 build_edge_index_np）
+│ ├── mesh.py # score → refined mesh
+│ ├── metrics.py # aw_rel / max_err
+│ ├── problem.py # PDE 参数 → HelmholtzProblem
+│ └── amr.py # 残差 AMR teacher
+│
+├── ckpt/ # checkpoint
+├── data_correction/ # 训练数据
+└── result/ # 评估结果
+```
+
+---
+
+## 10. 辅助模块
+
+| 模块 | 职责 |
+|------|------|
+| `rollout.py` | 统一 AMR rollout：`run_rollout_to_budget()` 驱动完整加密循环，支持 physics/neural/hybrid/eta 四种打分方法 |
+| `feat.py` | 构建 15 维基础特征 + budget_code |
+| `graph.py` | mesh → PyG Data（边特征 = phase_distance） |
+| `mesh.py` | score → 迭代 top-k 加密（叶子继承初始单元 score） |
+| `problem.py` | 参数字典 → HelmholtzProblem 实例 |
+| `amr.py` | 纯残差驱动 AMR teacher（无网络） |
+| `metrics.py` | `compute_mie_error`（aw_rel + max_err） |
+
+---
+
+## 11. 测试结果
+
+### 11.1 训练配置
+
+- 数据集：100 样本，~19 步/样本，1888 个 step 文件
+- 训练/验证划分：80/20（按 sample_id，seed=42）
+- 训练图：1513 个，验证图：375 个
+- 正样本比例：3.0%（teacher_mark top-3%）
+- 训练 100 epoch，最佳 epoch 57（val_loss=0.5873）
+
+### 11.2 离线指标（test_correction.py）
+
+在 20 个验证样本的 375 个 step 图上评估：
+
+| 指标 | GNN | Physics Baseline |
+|------|-----|-----------------|
+| **AUC** | **0.9412** | 0.0000 |
+| **top-k overlap 均值** | **0.440** | 0.131 |
+| GNN beats physics | **372/375 (99.2%)** | — |
+
+> Physics AUC=0.0 是因为 physics_score 在均匀网格上只有 2 个离散值，无法区分排序。GNN 通过学习 η 的空间分布模式，top-k overlap 提升 **3.4 倍**。
+
+### 11.3 Rollout 评估（eval_correction.py）
+
+20 个验证样本 × 3 种方法 × 3 个目标预算，每次 rollout 最终做 1 次 FEM solve：
+
+**aw_rel（面积加权相对误差）**：
+
+| 方法 | target=2000 | target=4000 | target=8000 |
+|------|------------|------------|------------|
+| physics | 19.19% | 14.04% | 13.25% |
+| neural | 15.96% | 13.72% | 12.98% |
+| **hybrid** | **15.78%** | **13.57%** | **12.94%** |
+
+**max_err（最大逐点误差）**：
+
+| 方法 | target=2000 | target=4000 | target=8000 |
+|------|------------|------------|------------|
+| physics | 0.3301 | 0.2514 | 0.2418 |
+| neural | 0.2741 | 0.2431 | 0.2376 |
+| **hybrid** | **0.2686** | **0.2430** | **0.2383** |
+
+**相对 physics-only 的改善**：
+
+| 方法 | target | aw_rel 改善 | max_err 改善 |
+|------|--------|-----------|-------------|
+| hybrid | 2000 | **+9.8%** | **+6.9%** |
+| neural | 2000 | +9.9% | +6.2% |
+| hybrid | 4000 | +1.9% | +1.5% |
+| neural | 4000 | +1.1% | +1.4% |
+| hybrid | 8000 | +1.9% | +1.3% |
+| neural | 8000 | +1.8% | +1.5% |
+
+### 11.4 关键发现
+
+1. **GNN 显著优于 physics baseline**：离线 top-k overlap 从 0.131 提升到 0.440（3.4×），99.2% 的验证图上 GNN 胜出
+2. **低预算改善最大**：target=2000 时 aw_rel 改善 ~10%，max_err 改善 ~7%；高预算时改善收窄到 ~2%（因为预算充足时 physics 也够用）
+3. **hybrid 略优于 neural**：z-score 混合策略在多数场景下比纯 GNN 更稳定
+4. **GNN 推理效率**：neural 方法比 physics 方法少用 ~12% 的 refinement 步数达到相同预算（8.9 vs 9.4 步 @2000），因为 GNN 的标记更精准
+
+### 11.5 OOD 评估（k 超出训练范围 [3,15]）
+
+固定 `eps_r=4, cx=cy=0.5, radius=0.15`，在 k=20/30/50/80 上做三方法对比（target=5000/10000/20000）：
+
+**aw_rel (%)**：
+
+| k | 方法 | target=5000 | target=10000 | target=20000 |
+|---|------|------------|-------------|-------------|
+| 20 | physics | 32.17 | 24.55 | 10.61 |
+| 20 | neural | 32.56 | **17.85** | 10.68 |
+| 20 | hybrid | **31.73** | 19.57 | 14.03 |
+| 30 | physics | 33.94 | 15.15 | 10.14 |
+| 30 | neural | **23.52** | 13.40 | 8.38 |
+| 30 | hybrid | 27.94 | **13.34** | **7.96** |
+| 50 | physics | 94.00 | 73.56 | 33.00 |
+| 50 | neural | **88.16** | **52.92** | **27.99** |
+| 50 | hybrid | 90.97 | 68.47 | 29.27 |
+| 80 | physics | 122.06 | 135.78 | 101.64 |
+| 80 | neural | 139.84 | **127.65** | **92.67** |
+| 80 | hybrid | 139.84 | 127.68 | 105.94 |
+
+**相对 physics-only 的改善 (%)**：
+
+| k | 方法 | target=5000 | target=10000 | target=20000 |
+|---|------|------------|-------------|-------------|
+| 20 | neural | −1.2 | **+27.3** | −0.7 |
+| 20 | hybrid | +1.4 | +20.3 | −32.3 |
+| 30 | neural | **+30.7** | +11.6 | +17.4 |
+| 30 | hybrid | +17.7 | +12.0 | +21.5 |
+| 50 | neural | +6.2 | **+28.1** | **+15.2** |
+| 50 | hybrid | +3.2 | +6.9 | +11.3 |
+| 80 | neural | −14.6 | +6.0 | **+8.8** |
+| 80 | hybrid | −14.6 | +6.0 | −4.2 |
+
+**OOD 关键发现**：
+
+1. **neural 在远 OOD（k=50）优势最大**：target=10000 时 aw_rel 从 73.56% 降至 52.92%（改善 +28.1%），hybrid 仅改善 +6.9%
+2. **hybrid 的 physics 先验在 OOD 时成为拖累**：z-score 混合中 physics_score 的 `max_edge/h_target` 在高 k 下不再准确，导致 hybrid 的标记不如纯 neural
+3. **neural 的泛化来自几何特征**：GNN 学到的是"界面附近 + 介质内 → 高密度"的空间模式，这一模式在 k 超出训练范围时仍然成立；而 physics_score 依赖 `lambda_eff = 2π/(k√ε_r)` 的具体数值
+4. **极端 OOD（k=80）两者都差**：误差超过 100%，说明 20000 个单元完全不够分辨 k=80 的短波结构（λ_eff≈0.028，需要 ~70000+ 单元）
+5. **k=20/30 时 hybrid 反而更好**：接近训练分布时 physics 先验有价值，hybrid 通过混合两种信号获得更稳定的标记
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diff --git a/outlook/analyze_budget_teacher.py b/outlook/analyze_budget_teacher.py
new file mode 100644
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--- /dev/null
+++ b/outlook/analyze_budget_teacher.py
@@ -0,0 +1,203 @@
+#!/usr/bin/env python3
+"""Analyze budgeted teacher dataset: per-budget stats, error improvement, saturation.
+
+Usage:
+ python outlook/analyze_budget_teacher.py
+ python outlook/analyze_budget_teacher.py --data-dir outlook/data/budget_density_dataset_check
+ python outlook/analyze_budget_teacher.py --sat-threshold 0.05
+"""
+
+import argparse
+from pathlib import Path
+
+import numpy as np
+
+
+def load_dataset(data_dir: Path):
+ """Load all sample .npz files, return list of dicts."""
+ data_dir = Path(data_dir)
+ params_path = data_dir / "params_list.npz"
+ if params_path.exists():
+ n_samples = len(np.load(params_path)["params"])
+ else:
+ # Fall back to scanning for numbered .npz files
+ n_samples = len(sorted(data_dir.glob("[0-9]*.npz")))
+
+ samples = []
+ for sid in range(n_samples):
+ npz_path = data_dir / f"{sid:04d}.npz"
+ if not npz_path.exists():
+ continue
+ d = np.load(npz_path)
+ samples.append({
+ "sid": sid,
+ "budgets": d["budgets"],
+ "actual_elements": d["actual_elements"],
+ "teacher_aw_rel": d["teacher_aw_rel"],
+ "teacher_max_err": d["teacher_max_err"],
+ "valid_budgets": d["valid_budgets"] if "valid_budgets" in d else np.ones(len(d["budgets"]), dtype=bool),
+ "match_ratios": d["match_ratios"] if "match_ratios" in d else d["actual_elements"] / d["budgets"],
+ "k": float(d["k"]),
+ "eps_r": float(d["eps_r"]),
+ })
+ return samples
+
+
+def per_budget_summary(samples):
+ """Aggregate stats grouped by budget value."""
+ groups = {} # budget -> list of sample dicts
+ for s in samples:
+ for bi, b in enumerate(s["budgets"]):
+ b = int(b)
+ groups.setdefault(b, {"aw_rel": [], "max_err": [], "actual": [], "valid": []})
+ groups[b]["aw_rel"].append(s["teacher_aw_rel"][bi])
+ groups[b]["max_err"].append(s["teacher_max_err"][bi])
+ groups[b]["actual"].append(s["actual_elements"][bi])
+ groups[b]["valid"].append(bool(s["valid_budgets"][bi]))
+
+ rows = []
+ for b in sorted(groups.keys()):
+ g = groups[b]
+ aw = np.array(g["aw_rel"])
+ me = np.array(g["max_err"])
+ rows.append({
+ "budget": b,
+ "n_samples": len(aw),
+ "n_valid": sum(g["valid"]),
+ "mean_actual": np.mean(g["actual"]),
+ "mean_aw_rel": np.mean(aw),
+ "std_aw_rel": np.std(aw),
+ "mean_max_err": np.mean(me),
+ })
+ return rows
+
+
+def compute_improvements(rows):
+ """Compute Δaw_rel and relative improvement between adjacent budgets."""
+ for i in range(len(rows)):
+ rows[i]["delta_aw_rel"] = None
+ rows[i]["rel_improvement"] = None
+ for i in range(1, len(rows)):
+ prev = rows[i - 1]["mean_aw_rel"]
+ curr = rows[i]["mean_aw_rel"]
+ delta = prev - curr # positive = improvement
+ rows[i]["delta_aw_rel"] = delta
+ rows[i]["rel_improvement"] = delta / prev if prev > 0 else 0.0
+ return rows
+
+
+def estimate_saturation(samples, threshold=0.02):
+ """For each sample, find the first budget where further improvement < threshold.
+
+ Saturation budget = first budget b such that
+ (aw_rel[b-1] - aw_rel[b]) / aw_rel[b-1] < threshold
+ i.e. relative improvement from previous budget is below threshold.
+
+ Returns list of (sid, saturation_budget, sat_reason).
+ """
+ results = []
+ for s in samples:
+ budgets = s["budgets"]
+ aw = s["teacher_aw_rel"]
+ sat_budget = None
+ for bi in range(1, len(budgets)):
+ if np.isnan(aw[bi - 1]) or np.isnan(aw[bi]):
+ continue
+ if aw[bi - 1] <= 0:
+ continue
+ rel_imp = (aw[bi - 1] - aw[bi]) / aw[bi - 1]
+ if rel_imp < threshold:
+ sat_budget = int(budgets[bi])
+ break
+ # If never saturated, mark as the largest budget
+ if sat_budget is None:
+ sat_budget = int(budgets[-1])
+ results.append({
+ "sid": s["sid"],
+ "saturation_budget": sat_budget,
+ })
+ return results
+
+
+def print_table(rows):
+ """Print the per-budget summary table."""
+ hdr = (f"{'budget':>8s} {'n':>4s} {'valid':>5s} "
+ f"{'mean_act':>9s} {'mean_aw':>9s} {'std_aw':>9s} {'mean_me':>9s} "
+ f"{'Δaw_rel':>9s} {'rel_imp':>9s}")
+ print(hdr)
+ print("-" * len(hdr))
+ for r in rows:
+ delta = f"{r['delta_aw_rel']:.6f}" if r["delta_aw_rel"] is not None else "—"
+ rel = f"{r['rel_improvement']:.4f}" if r["rel_improvement"] is not None else "—"
+ print(f"{r['budget']:8d} {r['n_samples']:4d} {r['n_valid']:5d} "
+ f"{r['mean_actual']:9.1f} {r['mean_aw_rel']:.6f} {r['std_aw_rel']:.6f} "
+ f"{r['mean_max_err']:.6f} {delta:>9s} {rel:>9s}")
+
+
+def print_saturation(sat_results, threshold):
+ """Print saturation budget distribution."""
+ budgets = [r["saturation_budget"] for r in sat_results]
+ unique = sorted(set(budgets))
+ print(f"\nSaturation budget distribution (threshold={threshold:.0%} rel. improvement):")
+ print(f" {'sat_budget':>12s} {'count':>6s} {'pct':>6s}")
+ for b in unique:
+ count = budgets.count(b)
+ pct = 100.0 * count / len(budgets)
+ print(f" {b:12d} {count:6d} {pct:5.1f}%")
+ print(f" {'median':>12s} {np.median(budgets):.0f}")
+ print(f" {'mean':>12s} {np.mean(budgets):.1f}")
+
+
+def main():
+ parser = argparse.ArgumentParser(description="Analyze budgeted teacher dataset")
+ parser.add_argument("--data-dir", type=str, default="outlook/data",
+ help="Path to budget dataset directory (default: outlook/data)")
+ parser.add_argument("--sat-threshold", type=float, default=0.02,
+ help="Relative improvement threshold for saturation (default: 0.02)")
+ parser.add_argument("--sat-threshold-2", type=float, default=0.05,
+ help="Second saturation threshold to report (default: 0.05)")
+ args = parser.parse_args()
+
+ data_dir = Path(args.data_dir)
+
+ print("=" * 70)
+ print("Budget Teacher Dataset Analysis")
+ print("=" * 70)
+ print(f" Data dir: {data_dir}")
+
+ samples = load_dataset(data_dir)
+ print(f" Samples: {len(samples)}")
+
+ budgets_all = samples[0]["budgets"]
+ print(f" Budgets: {[int(b) for b in budgets_all]}")
+ print()
+
+ # 1. Per-budget summary
+ rows = per_budget_summary(samples)
+ rows = compute_improvements(rows)
+
+ print("Per-budget summary:")
+ print_table(rows)
+
+ # 2. Saturation analysis
+ for thresh, label in [(args.sat_threshold, "primary"),
+ (args.sat_threshold_2, "secondary")]:
+ sat = estimate_saturation(samples, threshold=thresh)
+ print_saturation(sat, thresh)
+
+ # 3. Per-sample detail (compact)
+ print(f"\nPer-sample detail:")
+ print(f" {'sid':>4s} {'k':>6s} {'eps_r':>6s} "
+ + " ".join(f"b{int(b):>5d}" for b in budgets_all))
+ print(f" {'':>4s} {'':>6s} {'':>6s} "
+ + " ".join(f"{'aw_rel':>5s}" for _ in budgets_all))
+ print(" " + "-" * (20 + 8 * len(budgets_all)))
+ for s in samples:
+ vals = " ".join(f"{v:.4f}" for v in s["teacher_aw_rel"])
+ print(f" {s['sid']:4d} {s['k']:6.2f} {s['eps_r']:6.2f} {vals}")
+
+ print("\nDone.")
+
+
+if __name__ == "__main__":
+ main()
diff --git a/outlook/check_correction_data.py b/outlook/check_correction_data.py
new file mode 100644
index 0000000..e051760
--- /dev/null
+++ b/outlook/check_correction_data.py
@@ -0,0 +1,457 @@
+#!/usr/bin/env python3
+"""
+check_correction_data.py — Validate step-wise correction dataset.
+
+Checks:
+ 1. Global statistics (elements, marks, overlap, IoU, correction ratios)
+ 2. Per-step trend analysis (correction signal vs AMR step)
+ 3. Spatial visualization of 5 random samples
+ 4. Field & shape consistency
+ 5. Final verdict: PASS / WARNING / FAIL
+
+Usage:
+ python outlook/check_correction_data.py \
+ --data-dir outlook/data_correction \
+ --output-dir outlook/data_correction_check
+"""
+
+import argparse
+import sys
+from pathlib import Path
+
+import matplotlib
+matplotlib.use("Agg")
+import matplotlib.pyplot as plt
+import numpy as np
+
+# ──────────────────────────────────────────────────────────────────────────────
+# Required fields and their expected properties
+# ──────────────────────────────────────────────────────────────────────────────
+
+REQUIRED_FIELDS = {
+ "features": {"ndim": 2, "dtype_kind": "f"},
+ "edge_index": {"ndim": 2, "dtype_kind": "i"},
+ "physics_score": {"ndim": 1, "dtype_kind": "f"},
+ "teacher_eta": {"ndim": 1, "dtype_kind": "f"},
+ "teacher_mark": {"ndim": 1, "dtype_kind": "i"},
+ "physics_mark": {"ndim": 1, "dtype_kind": "i"},
+ "correction_label": {"ndim": 1, "dtype_kind": "i"},
+ "elements": {"ndim": 0},
+ "step": {"ndim": 0},
+ "aw_rel_before": {"ndim": 0},
+ "max_err_before": {"ndim": 0},
+ "k": {"ndim": 0},
+ "eps_r": {"ndim": 0},
+ "cx": {"ndim": 0},
+ "cy": {"ndim": 0},
+ "radius": {"ndim": 0},
+}
+
+
+# ──────────────────────────────────────────────────────────────────────────────
+# Helpers
+# ──────────────────────────────────────────────────────────────────────────────
+
+
+def iou_binary(a: np.ndarray, b: np.ndarray) -> float:
+ """IoU between two binary (0/1) arrays."""
+ a = a.astype(bool)
+ b = b.astype(bool)
+ inter = np.sum(a & b)
+ union = np.sum(a | b)
+ return float(inter) / float(union) if union > 0 else 1.0
+
+
+def load_all_samples(data_dir: Path):
+ """Load all sampleXXXX_stepYYY.npz files, return list of dicts."""
+ files = sorted(data_dir.glob("sample*_step*.npz"))
+ samples = []
+ for f in files:
+ try:
+ d = dict(np.load(f, allow_pickle=True))
+ d["_path"] = str(f)
+ d["_name"] = f.name
+ samples.append(d)
+ except Exception as e:
+ print(f" [WARN] Cannot load {f.name}: {e}")
+ return samples
+
+
+# ──────────────────────────────────────────────────────────────────────────────
+# 1. Field & shape consistency
+# ──────────────────────────────────────────────────────────────────────────────
+
+
+def check_fields(samples, issues):
+ """Check every file has the required fields with correct ndim."""
+ print("\n" + "=" * 70)
+ print(" [1/5] Field & Shape Consistency")
+ print("=" * 70)
+
+ n_files = len(samples)
+ n_issues_before = len(issues)
+
+ for s in samples:
+ name = s["_name"]
+ for field, spec in REQUIRED_FIELDS.items():
+ if field not in s:
+ issues.append(f"MISSING field '{field}' in {name}")
+ continue
+ arr = s[field]
+ if arr.ndim != spec["ndim"]:
+ issues.append(
+ f"BAD ndim for '{field}' in {name}: "
+ f"expected {spec['ndim']}, got {arr.ndim}"
+ )
+ if "dtype_kind" in spec and arr.dtype.kind != spec["dtype_kind"]:
+ issues.append(
+ f"BAD dtype for '{field}' in {name}: "
+ f"expected kind={spec['dtype_kind']}, got {arr.dtype}"
+ )
+
+ # Cross-check: features rows == len(physics_score) == elements
+ if "features" in s and "physics_score" in s:
+ nf = s["features"].shape[0]
+ ns = len(s["physics_score"])
+ ne = int(s["elements"])
+ if not (nf == ns == ne):
+ issues.append(
+ f"SIZE MISMATCH in {name}: features={nf}, "
+ f"physics_score={ns}, elements={ne}"
+ )
+
+ n_new = len(issues) - n_issues_before
+ if n_new == 0:
+ print(f" All {n_files} files have consistent fields & shapes.")
+ else:
+ print(f" Found {n_new} field/shape issues.")
+
+
+# ──────────────────────────────────────────────────────────────────────────────
+# 2. Global statistics
+# ──────────────────────────────────────────────────────────────────────────────
+
+
+def compute_global_stats(samples):
+ """Compute and print global statistics across all files."""
+ print("\n" + "=" * 70)
+ print(" [2/5] Global Statistics")
+ print("=" * 70)
+
+ elems = []
+ teacher_ratios = []
+ physics_ratios = []
+ overlaps = []
+ overlap_teacher = []
+ overlap_physics = []
+ ious = []
+ pos_ratios = []
+ neg_ratios = []
+
+ for s in samples:
+ n = int(s["elements"])
+ tm = s["teacher_mark"]
+ pm = s["physics_mark"]
+ cl = s["correction_label"]
+
+ elems.append(n)
+ n_tm = int(np.sum(tm))
+ n_pm = int(np.sum(pm))
+ ov = int(np.sum((tm == 1) & (pm == 1)))
+
+ teacher_ratios.append(n_tm / max(n, 1))
+ physics_ratios.append(n_pm / max(n, 1))
+ overlaps.append(ov)
+ overlap_teacher.append(ov / max(n_tm, 1))
+ overlap_physics.append(ov / max(n_pm, 1))
+ ious.append(iou_binary(tm, pm))
+ pos_ratios.append(int(np.sum(cl == 1)) / max(n, 1))
+ neg_ratios.append(int(np.sum(cl == -1)) / max(n, 1))
+
+ stats = {
+ "total_files": len(samples),
+ "elements": elems,
+ "teacher_mark_ratio": teacher_ratios,
+ "physics_mark_ratio": physics_ratios,
+ "overlap_count": overlaps,
+ "overlap/teacher": overlap_teacher,
+ "overlap/physics": overlap_physics,
+ "IoU": ious,
+ "correction_pos_ratio": pos_ratios,
+ "correction_neg_ratio": neg_ratios,
+ }
+
+ print(f" {'Metric':<30s} {'mean':>10s} {'min':>10s} {'max':>10s}")
+ print(f" {'-'*30} {'-'*10} {'-'*10} {'-'*10}")
+ for key in [
+ "elements", "teacher_mark_ratio", "physics_mark_ratio",
+ "overlap_count", "overlap/teacher", "overlap/physics",
+ "IoU", "correction_pos_ratio", "correction_neg_ratio",
+ ]:
+ arr = np.array(stats[key])
+ print(f" {key:<30s} {arr.mean():10.4f} {arr.min():10.4f} {arr.max():10.4f}")
+
+ return stats
+
+
+# ──────────────────────────────────────────────────────────────────────────────
+# 3. Per-step trend analysis
+# ──────────────────────────────────────────────────────────────────────────────
+
+
+def check_per_step_trends(samples, issues):
+ """Group by step, print trend table, flag anomalies."""
+ print("\n" + "=" * 70)
+ print(" [3/5] Per-Step Trend Analysis")
+ print("=" * 70)
+
+ from collections import defaultdict
+ step_data = defaultdict(lambda: {
+ "elems": [], "tm_ratio": [], "pm_ratio": [],
+ "overlap": [], "iou": [], "pos_ratio": [], "neg_ratio": [],
+ })
+
+ for s in samples:
+ step = int(s["step"])
+ n = int(s["elements"])
+ tm = s["teacher_mark"]
+ pm = s["physics_mark"]
+ cl = s["correction_label"]
+ n_tm = int(np.sum(tm))
+ n_pm = int(np.sum(pm))
+ ov = int(np.sum((tm == 1) & (pm == 1)))
+
+ d = step_data[step]
+ d["elems"].append(n)
+ d["tm_ratio"].append(n_tm / max(n, 1))
+ d["pm_ratio"].append(n_pm / max(n, 1))
+ d["overlap"].append(ov)
+ d["iou"].append(iou_binary(tm, pm))
+ d["pos_ratio"].append(int(np.sum(cl == 1)) / max(n, 1))
+ d["neg_ratio"].append(int(np.sum(cl == -1)) / max(n, 1))
+
+ steps = sorted(step_data.keys())
+ header = f" {'step':>4s} {'n_files':>7s} {'mean_elem':>9s} {'tm_ratio':>9s} {'pm_ratio':>9s} {'IoU':>7s} {'pos%':>7s} {'neg%':>7s}"
+ print(header)
+ print(f" {'-'*4} {'-'*7} {'-'*9} {'-'*9} {'-'*9} {'-'*7} {'-'*7} {'-'*7}")
+
+ for st in steps:
+ d = step_data[st]
+ nf = len(d["elems"])
+ me = np.mean(d["elems"])
+ mt = np.mean(d["tm_ratio"])
+ mp = np.mean(d["pm_ratio"])
+ mi = np.mean(d["iou"])
+ mpos = np.mean(d["pos_ratio"])
+ mneg = np.mean(d["neg_ratio"])
+ print(f" {st:4d} {nf:7d} {me:9.1f} {mt:9.4f} {mp:9.4f} {mi:7.4f} {mpos:7.4f} {mneg:7.4f}")
+
+ # Trend checks
+ if len(steps) >= 3:
+ # Check: correction signal should diminish at late steps (elements grow → marks shrink)
+ late = steps[-1]
+ early = steps[0]
+ late_pos = np.mean(step_data[late]["pos_ratio"])
+ early_pos = np.mean(step_data[early]["pos_ratio"])
+ late_neg = np.mean(step_data[late]["neg_ratio"])
+ early_neg = np.mean(step_data[early]["neg_ratio"])
+ late_iou = np.mean(step_data[late]["iou"])
+ early_iou = np.mean(step_data[early]["iou"])
+
+ print(f"\n Trend summary (step {early} → {late}):")
+ print(f" pos_ratio: {early_pos:.4f} → {late_pos:.4f}")
+ print(f" neg_ratio: {early_neg:.4f} → {late_neg:.4f}")
+ print(f" IoU: {early_iou:.4f} → {late_iou:.4f}")
+
+ # Warning: if late-step IoU is much lower than early, marks diverge
+ if late_iou < early_iou * 0.5:
+ issues.append(
+ f"TREND: IoU drops significantly from step {early} ({early_iou:.3f}) "
+ f"to step {late} ({late_iou:.3f}) — marks diverge at late steps."
+ )
+
+ # Warning: if correction signal vanishes (pos+neg → 0) at late steps
+ late_corr = late_pos + late_neg
+ early_corr = early_pos + early_neg
+ if early_corr > 0.01 and late_corr < early_corr * 0.1:
+ issues.append(
+ f"TREND: Correction signal nearly vanishes at step {late} "
+ f"({late_corr:.4f}) vs step {early} ({early_corr:.4f})."
+ )
+
+ # Warning: if IoU is very low overall (teacher and physics barely agree)
+ all_ious = [iou for s in steps for iou in step_data[s]["iou"]]
+ overall_iou = np.mean(all_ious)
+ if overall_iou < 0.1:
+ issues.append(
+ f"LOW IoU: mean IoU across all steps is {overall_iou:.4f} — "
+ f"teacher_mark and physics_mark barely overlap."
+ )
+
+
+# ──────────────────────────────────────────────────────────────────────────────
+# 4. Spatial visualization
+# ──────────────────────────────────────────────────────────────────────────────
+
+
+def plot_spatial_samples(samples, output_dir: Path, n_plot: int = 5):
+ """Randomly select n_plot files and save 4-panel spatial maps."""
+ print("\n" + "=" * 70)
+ print(" [4/5] Spatial Visualization")
+ print("=" * 70)
+
+ output_dir.mkdir(parents=True, exist_ok=True)
+
+ rng = np.random.RandomState(1234)
+ indices = rng.choice(len(samples), size=min(n_plot, len(samples)), replace=False)
+ selected = [samples[i] for i in sorted(indices)]
+
+ for s in selected:
+ name = s["_name"].replace(".npz", "")
+ features = s["features"]
+ x = features[:, 0]
+ y = features[:, 1]
+
+ physics_score = s["physics_score"]
+ teacher_eta = s["teacher_eta"]
+ teacher_mark = s["teacher_mark"]
+ correction_label = s["correction_label"]
+
+ fig, axes = plt.subplots(1, 4, figsize=(20, 5))
+ fig.suptitle(
+ f"{name} (elem={int(s['elements'])}, k={float(s['k']):.2f}, "
+ f"step={int(s['step'])})",
+ fontsize=12,
+ )
+
+ # Panel 1: physics_score
+ sc0 = axes[0].scatter(x, y, c=physics_score, s=8, cmap="viridis")
+ axes[0].set_title("physics_score")
+ axes[0].set_aspect("equal")
+ plt.colorbar(sc0, ax=axes[0], shrink=0.8)
+
+ # Panel 2: teacher_eta
+ sc1 = axes[1].scatter(x, y, c=teacher_eta, s=8, cmap="magma")
+ axes[1].set_title("teacher_eta")
+ axes[1].set_aspect("equal")
+ plt.colorbar(sc1, ax=axes[1], shrink=0.8)
+
+ # Panel 3: teacher_mark
+ sc2 = axes[2].scatter(x, y, c=teacher_mark, s=8, cmap="Reds", vmin=0, vmax=1)
+ axes[2].set_title("teacher_mark")
+ axes[2].set_aspect("equal")
+ plt.colorbar(sc2, ax=axes[2], shrink=0.8)
+
+ # Panel 4: correction_label
+ sc3 = axes[3].scatter(
+ x, y, c=correction_label, s=8, cmap="coolwarm", vmin=-1, vmax=1
+ )
+ axes[3].set_title("correction_label")
+ axes[3].set_aspect("equal")
+ plt.colorbar(sc3, ax=axes[3], shrink=0.8)
+
+ for ax in axes:
+ ax.set_xlabel("x")
+ ax.set_ylabel("y")
+
+ plt.tight_layout()
+ out_path = output_dir / f"{name}.png"
+ fig.savefig(out_path, dpi=150, bbox_inches="tight")
+ plt.close(fig)
+ print(f" ✓ Saved: {out_path}")
+
+
+# ──────────────────────────────────────────────────────────────────────────────
+# 5. Verdict
+# ──────────────────────────────────────────────────────────────────────────────
+
+
+def print_verdict(issues):
+ """Print final PASS / WARNING / FAIL."""
+ print("\n" + "=" * 70)
+ print(" [5/5] Verdict")
+ print("=" * 70)
+
+ if not issues:
+ print("\n ✅ PASS — Data is consistent and ready for training.")
+ return "PASS"
+
+ # Classify issues
+ errors = [i for i in issues if any(k in i.upper() for k in ["MISSING", "BAD ", "MISMATCH"])]
+ warnings = [i for i in issues if i not in errors]
+
+ if errors:
+ print(f"\n ❌ FAIL — {len(errors)} error(s) found:")
+ for e in errors:
+ print(f" • {e}")
+ if warnings:
+ print(f"\n ⚠️ Also {len(warnings)} warning(s):")
+ for w in warnings:
+ print(f" • {w}")
+ return "FAIL"
+
+ print(f"\n ⚠️ WARNING — {len(warnings)} suspicious pattern(s):")
+ for w in warnings:
+ print(f" • {w}")
+ return "WARNING"
+
+
+# ──────────────────────────────────────────────────────────────────────────────
+# Main
+# ──────────────────────────────────────────────────────────────────────────────
+
+
+def main():
+ parser = argparse.ArgumentParser(
+ description="Check step-wise correction dataset quality"
+ )
+ parser.add_argument(
+ "--data-dir", type=str, required=True,
+ help="Directory containing sampleXXXX_stepYYY.npz files",
+ )
+ parser.add_argument(
+ "--output-dir", type=str, default="outlook/data_correction_check",
+ help="Directory to save visualization plots",
+ )
+ args = parser.parse_args()
+
+ data_dir = Path(args.data_dir)
+ output_dir = Path(args.output_dir)
+
+ print("=" * 70)
+ print(" Correction Data Quality Check")
+ print("=" * 70)
+ print(f" Data dir: {data_dir}")
+ print(f" Output dir: {output_dir}")
+
+ # Load
+ print("\n Loading files...")
+ samples = load_all_samples(data_dir)
+ if not samples:
+ print(" ✗ No sample files found!")
+ sys.exit(1)
+ print(f" Loaded {len(samples)} files.")
+
+ issues = []
+
+ # 1. Field consistency
+ check_fields(samples, issues)
+
+ # 2. Global stats
+ compute_global_stats(samples)
+
+ # 3. Per-step trends
+ check_per_step_trends(samples, issues)
+
+ # 4. Visualization
+ plot_spatial_samples(samples, output_dir)
+
+ # 5. Verdict
+ verdict = print_verdict(issues)
+
+ print()
+ return 0 if verdict == "PASS" else 1
+
+
+if __name__ == "__main__":
+ sys.exit(main())
diff --git a/outlook/ckpt/budgeted_debug.json b/outlook/ckpt/budgeted_debug.json
new file mode 100644
index 0000000..65a44ca
--- /dev/null
+++ b/outlook/ckpt/budgeted_debug.json
@@ -0,0 +1,47 @@
+{
+ "config": {
+ "data_dir": "outlook/data/budget_density_dataset_debug",
+ "epochs": 2,
+ "batch_size": 2,
+ "lr": 0.001,
+ "density_weight": 1.0,
+ "mono_weight": 0.0,
+ "seed": 42
+ },
+ "per_budget": {
+ "budget_1000": {
+ "mse": 2.209566116333008,
+ "corr": -0.5653519502499024,
+ "top20_overlap": 0.037037037037037035,
+ "n_graphs": 1
+ },
+ "budget_2000": {
+ "mse": 4.281199932098389,
+ "corr": -0.4546216071701198,
+ "top20_overlap": 0.07407407407407407,
+ "n_graphs": 1
+ },
+ "overall": {
+ "mse": 3.2453832626342773,
+ "corr": -0.4747666722392795
+ }
+ },
+ "training_log": [
+ {
+ "epoch": 0,
+ "train_loss": 10.175954818725586,
+ "val_loss": 3.5997772216796875,
+ "val_corr": -0.5083683560193551,
+ "val_top20_overlap": 0.07407407407407407,
+ "lr": 0.001
+ },
+ {
+ "epoch": 1,
+ "train_loss": 7.313832759857178,
+ "val_loss": 3.2453830242156982,
+ "val_corr": -0.4747666660841676,
+ "val_top20_overlap": 0.05555555555555555,
+ "lr": 0.001
+ }
+ ]
+}
\ No newline at end of file
diff --git a/outlook/ckpt/budgeted_debug.pt b/outlook/ckpt/budgeted_debug.pt
new file mode 100644
index 0000000..98918ca
Binary files /dev/null and b/outlook/ckpt/budgeted_debug.pt differ
diff --git a/outlook/ckpt/correction.pt b/outlook/ckpt/correction.pt
new file mode 100644
index 0000000..300d12c
Binary files /dev/null and b/outlook/ckpt/correction.pt differ
diff --git a/outlook/ckpt/correction_best.pt b/outlook/ckpt/correction_best.pt
new file mode 100644
index 0000000..3ae222a
Binary files /dev/null and b/outlook/ckpt/correction_best.pt differ
diff --git a/outlook/ckpt/correction_train_log.json b/outlook/ckpt/correction_train_log.json
new file mode 100644
index 0000000..c9076b6
--- /dev/null
+++ b/outlook/ckpt/correction_train_log.json
@@ -0,0 +1,902 @@
+[
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diff --git a/outlook/data_correction/summary.json b/outlook/data_correction/summary.json
new file mode 100644
index 0000000..7fae4e3
--- /dev/null
+++ b/outlook/data_correction/summary.json
@@ -0,0 +1,10 @@
+{
+ "total_steps": 1888,
+ "total_files": 1888,
+ "mean_elements": 3497.1530720338983,
+ "mean_teacher_mark_ratio": 0.02968902442738579,
+ "mean_physics_mark_ratio": 0.02968902442738579,
+ "mean_overlap_teacher_physics": 15.933262711864407,
+ "mean_correction_pos_ratio": 0.024622349172869883,
+ "mean_correction_neg_ratio": 0.024622349172869883
+}
\ No newline at end of file
diff --git a/outlook/data_correction_check/sample0001_step001.png b/outlook/data_correction_check/sample0001_step001.png
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index 0000000..201a3e5
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index 0000000..348f355
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diff --git a/outlook/data_correction_check/sample0027_step019.png b/outlook/data_correction_check/sample0027_step019.png
new file mode 100644
index 0000000..e3b8c1a
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diff --git a/outlook/data_correction_check/sample0039_step001.png b/outlook/data_correction_check/sample0039_step001.png
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index 0000000..e548868
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diff --git a/outlook/logs/correction_4581.err b/outlook/logs/correction_4581.err
new file mode 100644
index 0000000..b707c60
--- /dev/null
+++ b/outlook/logs/correction_4581.err
@@ -0,0 +1 @@
+slurmstepd: error: *** JOB 4581 ON node05 CANCELLED AT 2026-06-06T14:31:07 ***
diff --git a/outlook/logs/correction_4581.out b/outlook/logs/correction_4581.out
new file mode 100644
index 0000000..c0cf334
--- /dev/null
+++ b/outlook/logs/correction_4581.out
@@ -0,0 +1,26 @@
+============================================================
+Teacher-Mark Binary Classifier Training
+============================================================
+ Data dir: outlook/data_correction
+ Device: cuda
+ Epochs: 100
+ Batch size: 1
+ LR: 0.001
+ Latent dim: 64
+ MP steps: 3
+ Checkpoint: outlook/ckpt/correction.pt
+ Log: /public/home/dxw/Codes/afem/outlook/ckpt/correction_train_log.json
+
+Loading dataset...
+ Found 1998 files across 100 samples
+ Train samples: 80 Val samples: 20
+ Train: 1598 graphs, 2203757 nodes, 65355 positive (3.0%)
+ Val: 400 graphs, 513740 nodes, 15208 positive (3.0%)
+ Loaded in 5.7s
+
+Training...
+ Epoch 0 | train=0.9876 val=0.9234 | auc=0.8342 topk=0.216 phys=0.120 lr=1.00e-03
+ Epoch 10 | train=0.7189 val=0.7505 | auc=0.8856 topk=0.307 phys=0.120 lr=1.00e-03
+ Epoch 20 | train=0.6477 val=0.7192 | auc=0.8954 topk=0.312 phys=0.120 lr=1.00e-03
+ Epoch 30 | train=0.6108 val=0.7108 | auc=0.9025 topk=0.342 phys=0.120 lr=1.00e-03
+ Epoch 40 | train=0.5436 val=0.7289 | auc=0.9107 topk=0.357 phys=0.120 lr=5.00e-04
diff --git a/outlook/logs/correction_4582.err b/outlook/logs/correction_4582.err
new file mode 100644
index 0000000..e69de29
diff --git a/outlook/logs/correction_4582.out b/outlook/logs/correction_4582.out
new file mode 100644
index 0000000..e3b518c
--- /dev/null
+++ b/outlook/logs/correction_4582.out
@@ -0,0 +1,48 @@
+============================================================
+Teacher-Mark Binary Classifier Training
+============================================================
+ Data dir: outlook/data_correction
+ Device: cuda
+ Epochs: 100
+ Batch size: 32
+ LR: 0.001
+ Latent dim: 64
+ MP steps: 3
+ Checkpoint: outlook/ckpt/correction.pt
+ Log: /public/home/dxw/Codes/afem/outlook/ckpt/correction_train_log.json
+
+Loading dataset...
+ Found 1998 files across 100 samples
+ Train samples: 80 Val samples: 20
+ Train: 1598 graphs, 2203757 nodes, 65355 positive (3.0%)
+ Val: 400 graphs, 513740 nodes, 15208 positive (3.0%)
+ Loaded in 5.6s
+
+Training...
+ Epoch 0 | train=1.2278 val=1.1452 | auc=0.7556 topk=0.165 phys=0.120 lr=1.00e-03 | 3.5s
+ Epoch 10 | train=0.7870 val=0.8045 | auc=0.8856 topk=0.287 phys=0.120 lr=1.00e-03 | 1.9s
+ Epoch 20 | train=0.6734 val=0.7438 | auc=0.9029 topk=0.318 phys=0.120 lr=1.00e-03 | 1.9s
+ Epoch 30 | train=0.6258 val=0.7229 | auc=0.9079 topk=0.342 phys=0.120 lr=1.00e-03 | 1.9s
+ Epoch 40 | train=0.5536 val=0.7068 | auc=0.9134 topk=0.351 phys=0.120 lr=5.00e-04 | 1.9s
+ Epoch 50 | train=0.5223 val=0.7220 | auc=0.9140 topk=0.359 phys=0.120 lr=2.50e-04 | 1.9s
+ Epoch 60 | train=0.5032 val=0.7522 | auc=0.9117 topk=0.363 phys=0.120 lr=1.25e-04 | 1.9s
+ Epoch 70 | train=0.4880 val=0.7545 | auc=0.9127 topk=0.362 phys=0.120 lr=1.25e-04 | 1.9s
+ Epoch 80 | train=0.4804 val=0.7735 | auc=0.9121 topk=0.368 phys=0.120 lr=6.25e-05 | 1.9s
+ Epoch 90 | train=0.4763 val=0.7756 | auc=0.9121 topk=0.365 phys=0.120 lr=3.13e-05 | 1.9s
+ Epoch 99 | train=0.4737 val=0.7832 | auc=0.9116 topk=0.364 phys=0.120 lr=1.56e-05 | 1.9s
+
+Training completed in 191.7s
+
+Checkpoint saved: outlook/ckpt/correction.pt
+Training log saved: /public/home/dxw/Codes/afem/outlook/ckpt/correction_train_log.json
+
+============================================================
+Best epoch: 38
+ val_loss: 0.6904
+ val_auc: 0.9152
+ val_topk: 0.347
+ phys_topk: 0.120
+ GNN beats physics: YES
+============================================================
+
+Done.
diff --git a/outlook/logs/correction_4584.err b/outlook/logs/correction_4584.err
new file mode 100644
index 0000000..e69de29
diff --git a/outlook/logs/correction_4584.out b/outlook/logs/correction_4584.out
new file mode 100644
index 0000000..ce86a8a
--- /dev/null
+++ b/outlook/logs/correction_4584.out
@@ -0,0 +1,48 @@
+============================================================
+Teacher-Mark Binary Classifier Training
+============================================================
+ Data dir: outlook/data_correction
+ Device: cuda
+ Epochs: 100
+ Batch size: 32
+ LR: 0.001
+ Latent dim: 64
+ MP steps: 3
+ Checkpoint: outlook/ckpt/correction.pt
+ Log: /public/home/dxw/Codes/afem/outlook/ckpt/correction_train_log.json
+
+Loading dataset...
+ Found 1236 files across 100 samples
+ Train samples: 80 Val samples: 20
+ Train: 991 graphs, 5274265 nodes, 157771 positive (3.0%)
+ Val: 245 graphs, 1296751 nodes, 38781 positive (3.0%)
+ Loaded in 7.1s
+
+Training...
+ Epoch 0 | train=1.2012 val=1.1091 | auc=0.7760 topk=0.230 phys=0.153 lr=1.00e-03 | 4.7s
+ Epoch 10 | train=0.5825 val=0.6353 | auc=0.9287 topk=0.372 phys=0.153 lr=1.00e-03 | 3.2s
+ Epoch 20 | train=0.5019 val=0.5901 | auc=0.9378 topk=0.416 phys=0.153 lr=1.00e-03 | 3.2s
+ Epoch 30 | train=0.5124 val=0.5745 | auc=0.9417 topk=0.423 phys=0.153 lr=1.00e-03 | 3.1s
+ Epoch 40 | train=0.4355 val=0.5334 | auc=0.9498 topk=0.466 phys=0.153 lr=1.00e-03 | 3.2s
+ Epoch 50 | train=0.4143 val=0.5467 | auc=0.9520 topk=0.490 phys=0.153 lr=1.00e-03 | 3.2s
+ Epoch 60 | train=0.3744 val=0.5686 | auc=0.9506 topk=0.486 phys=0.153 lr=5.00e-04 | 3.2s
+ Epoch 70 | train=0.3544 val=0.5963 | auc=0.9510 topk=0.491 phys=0.153 lr=2.50e-04 | 3.1s
+ Epoch 80 | train=0.3443 val=0.6211 | auc=0.9505 topk=0.490 phys=0.153 lr=1.25e-04 | 3.3s
+ Epoch 90 | train=0.3419 val=0.6288 | auc=0.9502 topk=0.491 phys=0.153 lr=6.25e-05 | 3.2s
+ Epoch 99 | train=0.3382 val=0.6329 | auc=0.9501 topk=0.490 phys=0.153 lr=3.13e-05 | 3.2s
+
+Training completed in 321.8s
+
+Checkpoint saved: outlook/ckpt/correction.pt
+Training log saved: /public/home/dxw/Codes/afem/outlook/ckpt/correction_train_log.json
+
+============================================================
+Best epoch: 40
+ val_loss: 0.5334
+ val_auc: 0.9498
+ val_topk: 0.466
+ phys_topk: 0.153
+ GNN beats physics: YES
+============================================================
+
+Done.
diff --git a/outlook/logs/correction_4585.err b/outlook/logs/correction_4585.err
new file mode 100644
index 0000000..e69de29
diff --git a/outlook/logs/correction_4585.out b/outlook/logs/correction_4585.out
new file mode 100644
index 0000000..78172cf
--- /dev/null
+++ b/outlook/logs/correction_4585.out
@@ -0,0 +1,48 @@
+============================================================
+Teacher-Mark Binary Classifier Training
+============================================================
+ Data dir: outlook/data_correction
+ Device: cuda
+ Epochs: 100
+ Batch size: 32
+ LR: 0.001
+ Latent dim: 64
+ MP steps: 3
+ Checkpoint: outlook/ckpt/correction.pt
+ Log: /public/home/dxw/Codes/afem/outlook/ckpt/correction_train_log.json
+
+Loading dataset...
+ Found 1956 files across 100 samples
+ Train samples: 80 Val samples: 20
+ Train: 1568 graphs, 2258286 nodes, 66961 positive (3.0%)
+ Val: 388 graphs, 549666 nodes, 16295 positive (3.0%)
+ Loaded in 7.4s
+
+Training...
+ Epoch 0 | train=1.3072 val=1.2934 | auc=0.6305 topk=0.127 phys=0.102 lr=1.00e-03 | 3.3s | total=3.3s
+ Epoch 10 | train=0.8706 val=0.8948 | auc=0.8608 topk=0.258 phys=0.102 lr=1.00e-03 | 1.8s | total=21.9s
+ Epoch 20 | train=0.7636 val=0.8598 | auc=0.8790 topk=0.312 phys=0.102 lr=1.00e-03 | 1.9s | total=40.6s
+ Epoch 30 | train=0.6756 val=0.8004 | auc=0.8966 topk=0.319 phys=0.102 lr=1.00e-03 | 1.9s | total=59.2s
+ Epoch 40 | train=0.6571 val=0.7746 | auc=0.8983 topk=0.343 phys=0.102 lr=1.00e-03 | 1.9s | total=77.8s
+ Epoch 50 | train=0.5787 val=0.8101 | auc=0.9032 topk=0.366 phys=0.102 lr=5.00e-04 | 1.9s | total=96.4s
+ Epoch 60 | train=0.5457 val=0.8059 | auc=0.9075 topk=0.372 phys=0.102 lr=2.50e-04 | 1.9s | total=115.0s
+ Epoch 70 | train=0.5333 val=0.8503 | auc=0.9035 topk=0.372 phys=0.102 lr=1.25e-04 | 1.9s | total=133.6s
+ Epoch 80 | train=0.5197 val=0.8692 | auc=0.9021 topk=0.368 phys=0.102 lr=1.25e-04 | 1.8s | total=152.1s
+ Epoch 90 | train=0.5113 val=0.8570 | auc=0.9063 topk=0.375 phys=0.102 lr=6.25e-05 | 1.9s | total=170.7s
+ Epoch 99 | train=0.5058 val=0.8703 | auc=0.9036 topk=0.371 phys=0.102 lr=3.13e-05 | 1.9s | total=187.4s
+
+Training completed in 187.9s
+
+Checkpoint saved: outlook/ckpt/correction.pt
+Training log saved: /public/home/dxw/Codes/afem/outlook/ckpt/correction_train_log.json
+
+============================================================
+Best epoch: 37
+ val_loss: 0.7372
+ val_auc: 0.9060
+ val_topk: 0.343
+ phys_topk: 0.102
+ GNN beats physics: YES
+============================================================
+
+Done.
diff --git a/outlook/logs/correction_4586.err b/outlook/logs/correction_4586.err
new file mode 100644
index 0000000..e69de29
diff --git a/outlook/logs/correction_4586.out b/outlook/logs/correction_4586.out
new file mode 100644
index 0000000..e948dc3
--- /dev/null
+++ b/outlook/logs/correction_4586.out
@@ -0,0 +1,48 @@
+============================================================
+Teacher-Mark Binary Classifier Training
+============================================================
+ Data dir: outlook/data_correction
+ Device: cuda
+ Epochs: 100
+ Batch size: 32
+ LR: 0.001
+ Latent dim: 64
+ MP steps: 3
+ Checkpoint: outlook/ckpt/correction.pt
+ Log: /public/home/dxw/Codes/afem/outlook/ckpt/correction_train_log.json
+
+Loading dataset...
+ Found 1888 files across 100 samples
+ Train samples: 80 Val samples: 20
+ Train: 1513 graphs, 5301714 nodes, 158309 positive (3.0%)
+ Val: 375 graphs, 1300911 nodes, 38849 positive (3.0%)
+ Loaded in 11.4s
+
+Training...
+ Epoch 0 | train=1.2141 val=1.1141 | auc=0.7793 topk=0.182 phys=0.130 lr=1.00e-03 | 5.0s | total=5.0s
+ Epoch 10 | train=0.6835 val=0.7105 | auc=0.9103 topk=0.338 phys=0.130 lr=1.00e-03 | 3.4s | total=39.4s
+ Epoch 20 | train=0.6046 val=0.6748 | auc=0.9220 topk=0.370 phys=0.130 lr=1.00e-03 | 3.4s | total=73.5s
+ Epoch 30 | train=0.5223 val=0.6292 | auc=0.9316 topk=0.402 phys=0.130 lr=1.00e-03 | 3.4s | total=107.5s
+ Epoch 40 | train=0.4965 val=0.6377 | auc=0.9323 topk=0.421 phys=0.130 lr=1.00e-03 | 3.4s | total=141.5s
+ Epoch 50 | train=0.4445 val=0.6005 | auc=0.9408 topk=0.433 phys=0.130 lr=5.00e-04 | 3.4s | total=175.4s
+ Epoch 60 | train=0.4331 val=0.6315 | auc=0.9386 topk=0.438 phys=0.130 lr=5.00e-04 | 3.4s | total=209.4s
+ Epoch 70 | train=0.4120 val=0.6089 | auc=0.9432 topk=0.452 phys=0.130 lr=2.50e-04 | 3.4s | total=243.5s
+ Epoch 80 | train=0.4015 val=0.6321 | auc=0.9424 topk=0.455 phys=0.130 lr=1.25e-04 | 3.4s | total=277.7s
+ Epoch 90 | train=0.3970 val=0.6364 | auc=0.9422 topk=0.455 phys=0.130 lr=6.25e-05 | 3.4s | total=311.7s
+ Epoch 99 | train=0.3922 val=0.6449 | auc=0.9419 topk=0.454 phys=0.130 lr=6.25e-05 | 3.4s | total=342.5s
+
+Training completed in 343.1s
+
+Checkpoint saved: outlook/ckpt/correction.pt
+Training log saved: /public/home/dxw/Codes/afem/outlook/ckpt/correction_train_log.json
+
+============================================================
+Best epoch: 57
+ val_loss: 0.5873
+ val_auc: 0.9412
+ val_topk: 0.440
+ phys_topk: 0.130
+ GNN beats physics: YES
+============================================================
+
+Done.
diff --git a/outlook/output/build_pptx.py b/outlook/output/build_pptx.py
new file mode 100644
index 0000000..d4d4b4c
--- /dev/null
+++ b/outlook/output/build_pptx.py
@@ -0,0 +1,1071 @@
+#!/usr/bin/env python3
+"""
+Build GNN-AMR correction presentation PPTX from README content.
+Nature-style academic presentation, simplified Chinese.
+"""
+
+import json
+from pathlib import Path
+
+import numpy as np
+from pptx import Presentation
+from pptx.util import Inches, Pt, Emu
+from pptx.dml.color import RGBColor
+from pptx.enum.text import PP_ALIGN, MSO_ANCHOR
+from pptx.enum.shapes import MSO_SHAPE
+
+# ── Paths ──
+ROOT = Path(__file__).resolve().parent.parent.parent # afem/
+OUTLOOK = ROOT / "outlook"
+OUTPUT = OUTLOOK / "output"
+ASSETS = OUTPUT / "assets" / "figures"
+
+# ── Colors ──
+WHITE = RGBColor(0xFF, 0xFF, 0xFF)
+BG_LIGHT = RGBColor(0xF8, 0xF9, 0xFA)
+TEXT_DARK = RGBColor(0x1A, 0x1A, 0x2E)
+TEXT_MID = RGBColor(0x4A, 0x4A, 0x5A)
+TEXT_LIGHT = RGBColor(0x8A, 0x8A, 0x9A)
+ACCENT_BLUE = RGBColor(0x21, 0x96, 0xF3)
+ACCENT_RED = RGBColor(0xE9, 0x1E, 0x63)
+ACCENT_GREEN = RGBColor(0x4C, 0xAF, 0x50)
+ACCENT_ORANGE = RGBColor(0xFF, 0x98, 0x00)
+BORDER_LIGHT = RGBColor(0xE0, 0xE0, 0xE0)
+
+# ── Fonts ──
+FONT_CN = "Microsoft YaHei"
+FONT_EN = "Calibri"
+
+# ── Slide dimensions (16:9) ──
+SLIDE_W = Inches(13.333)
+SLIDE_H = Inches(7.5)
+
+
+def set_slide_bg(slide, color=BG_LIGHT):
+ """Set slide background color."""
+ bg = slide.background
+ fill = bg.fill
+ fill.solid()
+ fill.fore_color.rgb = color
+
+
+def add_shape_fill(slide, left, top, width, height, color, alpha=None):
+ """Add a colored rectangle shape."""
+ shape = slide.shapes.add_shape(MSO_SHAPE.RECTANGLE, left, top, width, height)
+ shape.fill.solid()
+ shape.fill.fore_color.rgb = color
+ shape.line.fill.background()
+ if alpha is not None:
+ shape.fill.fore_color.brightness = alpha
+ return shape
+
+
+def add_text_box(slide, left, top, width, height, text, font_size=14,
+ color=TEXT_DARK, bold=False, align=PP_ALIGN.LEFT,
+ font_name=FONT_CN, line_spacing=1.3):
+ """Add a text box with formatted text."""
+ txBox = slide.shapes.add_textbox(left, top, width, height)
+ tf = txBox.text_frame
+ tf.word_wrap = True
+ p = tf.paragraphs[0]
+ p.text = text
+ p.font.size = Pt(font_size)
+ p.font.color.rgb = color
+ p.font.bold = bold
+ p.font.name = font_name
+ p.alignment = align
+ p.space_after = Pt(2)
+ if line_spacing:
+ p.line_spacing = Pt(font_size * line_spacing)
+ return txBox
+
+
+def add_bullet_list(slide, left, top, width, height, items, font_size=14,
+ color=TEXT_DARK, font_name=FONT_CN, bullet_char="•"):
+ """Add a bulleted list."""
+ txBox = slide.shapes.add_textbox(left, top, width, height)
+ tf = txBox.text_frame
+ tf.word_wrap = True
+ for i, item in enumerate(items):
+ if i == 0:
+ p = tf.paragraphs[0]
+ else:
+ p = tf.add_paragraph()
+ p.text = f"{bullet_char} {item}"
+ p.font.size = Pt(font_size)
+ p.font.color.rgb = color
+ p.font.name = font_name
+ p.space_after = Pt(6)
+ p.line_spacing = Pt(font_size * 1.5)
+ return txBox
+
+
+def add_caption(slide, left, top, width, text, font_size=9, color=TEXT_LIGHT):
+ """Add a small caption/source line."""
+ return add_text_box(slide, left, top, width, Inches(0.3), text,
+ font_size=font_size, color=color)
+
+
+def add_takeaway_strip(slide, text, top=None):
+ """Add a bottom takeaway strip."""
+ if top is None:
+ top = SLIDE_H - Inches(0.6)
+ strip = add_shape_fill(slide, Inches(0), top, SLIDE_W, Inches(0.5),
+ RGBColor(0xE8, 0xF0, 0xFE))
+ add_text_box(slide, Inches(0.5), top + Inches(0.05), SLIDE_W - Inches(1),
+ Inches(0.4), f"✦ {text}", font_size=12, color=ACCENT_BLUE,
+ bold=True, align=PP_ALIGN.LEFT)
+
+
+def add_source_label(slide, text):
+ """Add source label at bottom-right."""
+ add_text_box(slide, SLIDE_W - Inches(4), SLIDE_H - Inches(0.35),
+ Inches(3.5), Inches(0.25), text,
+ font_size=8, color=TEXT_LIGHT, align=PP_ALIGN.RIGHT)
+
+
+def add_image_safe(slide, img_path, left, top, width, height):
+ """Add image if file exists, otherwise add placeholder."""
+ p = Path(img_path)
+ if p.exists() and p.stat().st_size > 0:
+ slide.shapes.add_picture(str(p), left, top, width, height)
+ else:
+ shape = add_shape_fill(slide, left, top, width, height, BORDER_LIGHT)
+ add_text_box(slide, left, top + height // 2 - Inches(0.2),
+ width, Inches(0.4), f"[{p.name}]", font_size=10,
+ color=TEXT_LIGHT, align=PP_ALIGN.CENTER)
+
+
+# ============================================================================
+# Slide builders
+# ============================================================================
+
+
+def slide_01_title(prs):
+ """Title slide."""
+ slide = prs.slides.add_slide(prs.slide_layouts[6]) # blank
+ set_slide_bg(slide, WHITE)
+
+ # Top accent bar
+ add_shape_fill(slide, Inches(0), Inches(0), SLIDE_W, Inches(0.08), ACCENT_BLUE)
+
+ # Title
+ add_text_box(slide, Inches(1), Inches(1.8), Inches(11), Inches(1.2),
+ "GNN 引导的自适应网格加密",
+ font_size=36, color=TEXT_DARK, bold=True, align=PP_ALIGN.CENTER)
+
+ # Subtitle
+ add_text_box(slide, Inches(1), Inches(3.1), Inches(11), Inches(0.8),
+ "用于 2D Helmholtz 散射问题的图神经网络修正学习",
+ font_size=20, color=TEXT_MID, align=PP_ALIGN.CENTER)
+
+ # Separator line
+ add_shape_fill(slide, Inches(5), Inches(4.2), Inches(3), Inches(0.03), ACCENT_BLUE)
+
+ # Meta
+ add_text_box(slide, Inches(1), Inches(4.6), Inches(11), Inches(0.5),
+ "Problem-to-Solution: 用 GNN 学习残差驱动 AMR 的修正信号",
+ font_size=14, color=TEXT_LIGHT, align=PP_ALIGN.CENTER)
+
+ add_text_box(slide, Inches(1), Inches(5.5), Inches(11), Inches(0.5),
+ "AFEM Research Group | 2026",
+ font_size=12, color=TEXT_LIGHT, align=PP_ALIGN.CENTER)
+
+
+def slide_02_background(prs):
+ """Research background."""
+ slide = prs.slides.add_slide(prs.slide_layouts[6])
+ set_slide_bg(slide, WHITE)
+
+ add_text_box(slide, Inches(0.6), Inches(0.4), Inches(12), Inches(0.7),
+ "研究背景：为什么这个问题重要",
+ font_size=28, color=TEXT_DARK, bold=True)
+
+ add_shape_fill(slide, Inches(0.6), Inches(1.1), Inches(2), Inches(0.04), ACCENT_BLUE)
+
+ # Left column: physics problem
+ add_text_box(slide, Inches(0.6), Inches(1.5), Inches(5.5), Inches(0.5),
+ "物理问题：2D 介质圆柱电磁散射", font_size=18, color=ACCENT_BLUE, bold=True)
+
+ add_bullet_list(slide, Inches(0.6), Inches(2.1), Inches(5.5), Inches(3.5), [
+ "求解散射场公式：∇²u + k²·ε_r·u = −k²·(ε_r−1)·u_inc",
+ "入射波 u_inc = exp(i·k·x)，Sommerfeld 辐射 BC",
+ "介质圆柱参数：k ∈ [3,15]，ε_r ∈ [2,8]，r ∈ [0.05,0.25]",
+ "FEM 求解器：P1 三角元 + Sommerfeld BC",
+ "参考解：Mie 解析解（精确对比基准）",
+ ], font_size=13)
+
+ # Right column: why it matters
+ add_text_box(slide, Inches(6.8), Inches(1.5), Inches(5.8), Inches(0.5),
+ "核心挑战：网格预算有限下的误差最小化",
+ font_size=18, color=ACCENT_RED, bold=True)
+
+ add_bullet_list(slide, Inches(6.8), Inches(2.1), Inches(5.8), Inches(3.5), [
+ "精细网格 → 高精度，但计算代价高",
+ "粗网格 → 快速，但误差大",
+ "目标：在给定网格预算 N 下，最小化 FEM 解误差",
+ "传统 AMR 需要逐步求解 FEM → 计算开销大",
+ "能否用数据驱动方法替代？",
+ ], font_size=13)
+
+ # Bottom box: parameter space
+ box = add_shape_fill(slide, Inches(0.6), Inches(5.6), Inches(12.1), Inches(1.2),
+ RGBColor(0xF0, 0xF4, 0xF8))
+ add_text_box(slide, Inches(0.8), Inches(5.7), Inches(11.5), Inches(0.4),
+ "参数空间", font_size=14, color=ACCENT_BLUE, bold=True)
+ add_text_box(slide, Inches(0.8), Inches(6.1), Inches(11.5), Inches(0.5),
+ "k ∈ [3,15] | ε_r ∈ [2,8] | cx, cy ∈ [0.2,0.8] | radius ∈ [0.05,0.25] | "
+ "统一初始网格 32×32 = 2048 单元",
+ font_size=12, color=TEXT_MID)
+
+
+def slide_03_gap(prs):
+ """Knowledge gap / bottleneck."""
+ slide = prs.slides.add_slide(prs.slide_layouts[6])
+ set_slide_bg(slide, WHITE)
+
+ add_text_box(slide, Inches(0.6), Inches(0.4), Inches(12), Inches(0.7),
+ "技术瓶颈：传统残差驱动 AMR 的局限",
+ font_size=28, color=TEXT_DARK, bold=True)
+
+ add_shape_fill(slide, Inches(0.6), Inches(1.1), Inches(2), Inches(0.04), ACCENT_RED)
+
+ # Left: traditional AMR
+ add_text_box(slide, Inches(0.6), Inches(1.5), Inches(5.5), Inches(0.5),
+ "传统残差驱动 AMR 流程", font_size=18, color=TEXT_MID, bold=True)
+
+ add_bullet_list(slide, Inches(0.6), Inches(2.1), Inches(5.5), Inches(3.0), [
+ "每步：FEM 求解 → 计算残差估计器 η → 标记 top-k → 加密",
+ "残差 η = √(r_int² + r_jump² + r_sbc²)",
+ "需要每步都做 FEM solve → 计算量大",
+ "η 是局部最优，不能利用全局几何/物理信息",
+ "无法离线推理：必须在线计算残差",
+ ], font_size=13)
+
+ # Right: what we want
+ add_text_box(slide, Inches(6.8), Inches(1.5), Inches(5.8), Inches(0.5),
+ "我们希望实现", font_size=18, color=ACCENT_GREEN, bold=True)
+
+ add_bullet_list(slide, Inches(6.8), Inches(2.1), Inches(5.8), Inches(3.0), [
+ "用 GNN 学习 \"哪些单元应被加密\"",
+ "推理时只需几何/物理特征 → 无需 FEM solve",
+ "一次前向传播 → 全图单元标记",
+ "可离线部署，计算代价大幅降低",
+ "超越纯物理先验的标记策略",
+ ], font_size=13)
+
+ # Bottom: key insight
+ box = add_shape_fill(slide, Inches(0.6), Inches(5.3), Inches(12.1), Inches(1.5),
+ RGBColor(0xFE, 0xF3, 0xE2))
+ add_text_box(slide, Inches(0.8), Inches(5.4), Inches(11.5), Inches(0.4),
+ "核心洞察", font_size=14, color=ACCENT_ORANGE, bold=True)
+ add_text_box(slide, Inches(0.8), Inches(5.85), Inches(11.5), Inches(0.8),
+ "物理先验 physics_score = h/λ_eff 可以粗略判断分辨率不足的单元，但它忽略了散射体几何、"
+ "波场相位、材料界面等关键信息。GNN 可以学习这些物理先验无法捕捉的修正信号。",
+ font_size=13, color=TEXT_MID)
+
+
+def slide_04_approach(prs):
+ """Core approach: correction learning."""
+ slide = prs.slides.add_slide(prs.slide_layouts[6])
+ set_slide_bg(slide, WHITE)
+
+ add_text_box(slide, Inches(0.6), Inches(0.4), Inches(12), Inches(0.7),
+ "核心思路：GNN 学习修正信号",
+ font_size=28, color=TEXT_DARK, bold=True)
+
+ add_shape_fill(slide, Inches(0.6), Inches(1.1), Inches(2), Inches(0.04), ACCENT_GREEN)
+
+ # Three mark schemes
+ add_text_box(slide, Inches(0.6), Inches(1.5), Inches(12), Inches(0.5),
+ "三种标记方案的对比", font_size=18, color=TEXT_MID, bold=True)
+
+ # Three boxes
+ box_w = Inches(3.7)
+ box_h = Inches(2.8)
+ gap = Inches(0.35)
+ x0 = Inches(0.6)
+ y_top = Inches(2.2)
+
+ # Box 1: teacher
+ b1 = add_shape_fill(slide, x0, y_top, box_w, box_h, RGBColor(0xE8, 0xF5, 0xE9))
+ add_text_box(slide, x0 + Inches(0.15), y_top + Inches(0.1), box_w - Inches(0.3), Inches(0.4),
+ "teacher_mark (η 信号)", font_size=14, color=ACCENT_GREEN, bold=True)
+ add_bullet_list(slide, x0 + Inches(0.15), y_top + Inches(0.55), box_w - Inches(0.3), Inches(2.0), [
+ "基于残差估计器 η 排序",
+ "取 top 3% 单元标记为 1",
+ "需要 FEM solve → 计算代价高",
+ "代表 \"最优\" 加密决策",
+ ], font_size=12, color=TEXT_MID, bullet_char="▸")
+
+ # Box 2: physics
+ b2 = add_shape_fill(slide, x0 + box_w + gap, y_top, box_w, box_h, RGBColor(0xE3, 0xF2, 0xFD))
+ add_text_box(slide, x0 + box_w + gap + Inches(0.15), y_top + Inches(0.1),
+ box_w - Inches(0.3), Inches(0.4),
+ "physics_score (物理先验)", font_size=14, color=ACCENT_BLUE, bold=True)
+ add_bullet_list(slide, x0 + box_w + gap + Inches(0.15), y_top + Inches(0.55),
+ box_w - Inches(0.3), Inches(2.0), [
+ "h / λ_eff，纯几何计算",
+ "无需 FEM solve",
+ "忽略波场、几何、材料信息",
+ "基线对比方法",
+ ], font_size=12, color=TEXT_MID, bullet_char="▸")
+
+ # Box 3: correction
+ b3 = add_shape_fill(slide, x0 + 2 * (box_w + gap), y_top, box_w, box_h, RGBColor(0xFC, 0xE4, 0xEC))
+ add_text_box(slide, x0 + 2 * (box_w + gap) + Inches(0.15), y_top + Inches(0.1),
+ box_w - Inches(0.3), Inches(0.4),
+ "correction_label (GNN 目标)", font_size=14, color=ACCENT_RED, bold=True)
+ add_bullet_list(slide, x0 + 2 * (box_w + gap) + Inches(0.15), y_top + Inches(0.55),
+ box_w - Inches(0.3), Inches(2.0), [
+ "= teacher_mark − physics_mark",
+ "+1：teacher 独有（应加密）",
+ " 0：两者一致",
+ "−1：physics 独有（不应加密）",
+ ], font_size=12, color=TEXT_MID, bullet_char="▸")
+
+ # Bottom takeaway
+ add_takeaway_strip(slide,
+ "GNN 的训练目标：学习 teacher 与 physics 之间的差异，使标记策略超越纯物理先验")
+
+
+def slide_05_pipeline(prs):
+ """Full pipeline overview."""
+ slide = prs.slides.add_slide(prs.slide_layouts[6])
+ set_slide_bg(slide, WHITE)
+
+ add_text_box(slide, Inches(0.6), Inches(0.4), Inches(12), Inches(0.7),
+ "全流程概览：5 步流水线",
+ font_size=28, color=TEXT_DARK, bold=True)
+
+ add_shape_fill(slide, Inches(0.6), Inches(1.1), Inches(2), Inches(0.04), ACCENT_BLUE)
+
+ # Pipeline steps as connected boxes
+ steps = [
+ ("Step 1", "数据生成", "gen.py", "残差驱动 AMR\n保存逐步数据 + 标签", ACCENT_BLUE),
+ ("Step 2", "数据校验", "check.py", "字段完整性\n统计趋势\n空间可视化", ACCENT_GREEN),
+ ("Step 3", "训练", "train.py", "features + physics_score\n→ GNN → sigmoid\n→ 二分类", ACCENT_RED),
+ ("Step 4", "评估", "test/eval.py", "离线指标 + Rollout\n三种方法对比", ACCENT_ORANGE),
+ ("Step 5", "可视化", "viz.py", "端到端 AMR\n单步对比", RGBColor(0x9C, 0x27, 0xB0)),
+ ]
+
+ box_w = Inches(2.2)
+ box_h = Inches(3.2)
+ x_start = Inches(0.5)
+ y_top = Inches(1.6)
+ gap = Inches(0.3)
+
+ for i, (step_num, title, script, desc, color) in enumerate(steps):
+ x = x_start + i * (box_w + gap)
+
+ # Step number circle
+ circle = slide.shapes.add_shape(MSO_SHAPE.OVAL, x + Inches(0.8), y_top, Inches(0.6), Inches(0.6))
+ circle.fill.solid()
+ circle.fill.fore_color.rgb = color
+ circle.line.fill.background()
+ tf = circle.text_frame
+ tf.paragraphs[0].text = str(i + 1)
+ tf.paragraphs[0].font.size = Pt(18)
+ tf.paragraphs[0].font.color.rgb = WHITE
+ tf.paragraphs[0].font.bold = True
+ tf.paragraphs[0].alignment = PP_ALIGN.CENTER
+ tf.word_wrap = False
+
+ # Title
+ add_text_box(slide, x, y_top + Inches(0.7), box_w, Inches(0.4),
+ title, font_size=16, color=color, bold=True, align=PP_ALIGN.CENTER)
+
+ # Script name
+ add_text_box(slide, x, y_top + Inches(1.1), box_w, Inches(0.3),
+ script, font_size=10, color=TEXT_LIGHT, align=PP_ALIGN.CENTER,
+ font_name=FONT_EN)
+
+ # Description
+ add_text_box(slide, x + Inches(0.1), y_top + Inches(1.5), box_w - Inches(0.2), Inches(1.8),
+ desc, font_size=11, color=TEXT_MID, align=PP_ALIGN.CENTER)
+
+ # Arrow between steps
+ if i < len(steps) - 1:
+ arrow_x = x + box_w + Inches(0.05)
+ arrow_y = y_top + Inches(0.25)
+ add_text_box(slide, arrow_x, arrow_y, Inches(0.2), Inches(0.3),
+ "→", font_size=20, color=TEXT_LIGHT, align=PP_ALIGN.CENTER)
+
+ # Bottom: key data flow
+ box = add_shape_fill(slide, Inches(0.5), Inches(5.3), Inches(12.3), Inches(1.5),
+ RGBColor(0xF5, 0xF5, 0xF5))
+ add_text_box(slide, Inches(0.7), Inches(5.4), Inches(11.8), Inches(0.4),
+ "数据流", font_size=14, color=ACCENT_BLUE, bold=True)
+ add_text_box(slide, Inches(0.7), Inches(5.85), Inches(11.8), Inches(0.8),
+ "PDE 参数采样 → 初始网格 → AMR 循环（FEM solve → η → marks → save → refine）→ "
+ "训练数据 (.npz) → GNN 训练 → checkpoint → 离线推理 / Rollout 评估 → 可视化",
+ font_size=12, color=TEXT_MID)
+
+
+def slide_06_data(prs):
+ """Data generation and marking strategy."""
+ slide = prs.slides.add_slide(prs.slide_layouts[6])
+ set_slide_bg(slide, WHITE)
+
+ add_text_box(slide, Inches(0.6), Inches(0.4), Inches(12), Inches(0.7),
+ "Step 1：数据生成与标记策略",
+ font_size=28, color=TEXT_DARK, bold=True)
+
+ add_shape_fill(slide, Inches(0.6), Inches(1.1), Inches(2), Inches(0.04), ACCENT_BLUE)
+
+ # Left: data generation flow
+ add_text_box(slide, Inches(0.6), Inches(1.5), Inches(5.5), Inches(0.5),
+ "残差驱动 AMR 循环", font_size=18, color=TEXT_MID, bold=True)
+
+ add_bullet_list(slide, Inches(0.6), Inches(2.1), Inches(5.5), Inches(2.5), [
+ "100 个 PDE 样本，统一初始网格 32×32",
+ "每步：FEM solve → 残差 η → 三种标记 → 保存 → 加密",
+ "每步保存 .npz：15-dim 特征 + 边索引 + 标记",
+ "共 1236 个 step 文件，平均 ~12 步/样本",
+ "加密时使用安全过滤：面积 + 反向 Dörfler",
+ ], font_size=13)
+
+ # Right: residual estimator
+ add_text_box(slide, Inches(6.8), Inches(1.5), Inches(5.8), Inches(0.5),
+ "残差估计器 η（Teacher Signal）",
+ font_size=18, color=TEXT_MID, bold=True)
+
+ add_bullet_list(slide, Inches(6.8), Inches(2.1), Inches(5.8), Inches(2.5), [
+ "η = √(r_int² + r_jump² + r_sbc²)",
+ "r_int：内部残差（PDE 残差 × h/k）",
+ "r_jump：梯度跳变（相邻单元边界）",
+ "r_sbc：Sommerfeld BC 边界残差",
+ "使用 k₀ 归一化，介质内短波残差自然放大",
+ ], font_size=13)
+
+ # Bottom: data check visualization
+ add_image_safe(slide, OUTLOOK / "data_correction_check" / "sample0011_step002.png",
+ Inches(0.6), Inches(4.6), Inches(12.1), Inches(2.4))
+ add_source_label(slide, "Source: check_correction_data.py — 4 面板空间可视化")
+
+
+def slide_07_features(prs):
+ """Feature engineering."""
+ slide = prs.slides.add_slide(prs.slide_layouts[6])
+ set_slide_bg(slide, WHITE)
+
+ add_text_box(slide, Inches(0.6), Inches(0.4), Inches(12), Inches(0.7),
+ "Step 1：15 维特征工程",
+ font_size=28, color=TEXT_DARK, bold=True)
+
+ add_shape_fill(slide, Inches(0.6), Inches(1.1), Inches(2), Inches(0.04), ACCENT_BLUE)
+
+ # Feature table
+ features = [
+ ("0, 1", "x, y", "单元中点坐标"),
+ ("2", "area", "单元面积"),
+ ("3", "dist_to_center", "到圆柱中心距离"),
+ ("4", "signed_dist", "dist − radius（负值=介质内）"),
+ ("5", "inside", "是否在圆柱内 (0/1)"),
+ ("6", "k", "波数（全局常量）"),
+ ("7", "eps_r", "介电常数（全局常量）"),
+ ("8", "radius", "半径（全局常量）"),
+ ("9, 10", "cx, cy", "圆柱中心（全局常量）"),
+ ("11", "k_h", "k × √area（网格-波数耦合）"),
+ ("12", "k_eps_h", "k × √eps_r × √area（介质内分辨率）"),
+ ("13", "sin(k·x)", "入射波相位 sin 分量"),
+ ("14", "cos(k·x)", "入射波相位 cos 分量"),
+ ]
+
+ # Table header
+ y_start = Inches(1.5)
+ row_h = Inches(0.32)
+ col_widths = [Inches(0.8), Inches(2.0), Inches(5.5)]
+ x_start = Inches(0.6)
+
+ # Header
+ header_bg = add_shape_fill(slide, x_start, y_start,
+ sum(w for w in col_widths), row_h, ACCENT_BLUE)
+ headers = ["维度", "特征名", "说明"]
+ x = x_start
+ for j, (hdr, w) in enumerate(zip(headers, col_widths)):
+ add_text_box(slide, x, y_start + Inches(0.02), w, row_h,
+ hdr, font_size=11, color=WHITE, bold=True, align=PP_ALIGN.CENTER)
+ x += w
+
+ # Rows
+ for i, (dim, name, desc) in enumerate(features):
+ y = y_start + (i + 1) * row_h
+ bg_color = RGBColor(0xF8, 0xF9, 0xFA) if i % 2 == 0 else WHITE
+ add_shape_fill(slide, x_start, y, sum(w for w in col_widths), row_h, bg_color)
+
+ x = x_start
+ vals = [dim, name, desc]
+ for j, (val, w) in enumerate(zip(vals, col_widths)):
+ font_name = FONT_EN if j < 2 else FONT_CN
+ add_text_box(slide, x, y + Inches(0.02), w, row_h,
+ val, font_size=10, color=TEXT_DARK,
+ align=PP_ALIGN.CENTER if j < 2 else PP_ALIGN.LEFT,
+ font_name=font_name)
+ x += w
+
+ # Right: physics score
+ box_x = Inches(9.2)
+ box = add_shape_fill(slide, box_x, Inches(1.5), Inches(3.5), Inches(3.5),
+ RGBColor(0xE8, 0xF0, 0xFE))
+ add_text_box(slide, box_x + Inches(0.15), Inches(1.6), Inches(3.2), Inches(0.4),
+ "Physics Score（第 16 维输入）", font_size=13, color=ACCENT_BLUE, bold=True)
+ add_text_box(slide, box_x + Inches(0.15), Inches(2.1), Inches(3.2), Inches(2.5),
+ "λ_eff = 2π/(k·√ε_r) 介质内\n"
+ " = 2π/k 介质外\n\n"
+ "h = √(2·area) 特征长度\n\n"
+ "physics_score = h / λ_eff\n\n"
+ "> 1 表示分辨率不足\n"
+ "→ 应优先加密",
+ font_size=11, color=TEXT_MID, font_name=FONT_EN)
+
+ # Bottom: normalization
+ add_takeaway_strip(slide,
+ "训练时 15-dim 特征 + physics_score = 16-dim 输入，z-score 归一化")
+
+
+def slide_08_gnn(prs):
+ """GNN architecture."""
+ slide = prs.slides.add_slide(prs.slide_layouts[6])
+ set_slide_bg(slide, WHITE)
+
+ add_text_box(slide, Inches(0.6), Inches(0.4), Inches(12), Inches(0.7),
+ "Step 3：CorrectionGNN 架构",
+ font_size=28, color=TEXT_DARK, bold=True)
+
+ add_shape_fill(slide, Inches(0.6), Inches(1.1), Inches(2), Inches(0.04), ACCENT_RED)
+
+ # Architecture diagram as text boxes
+ # Embedding layer
+ add_text_box(slide, Inches(0.6), Inches(1.5), Inches(5.5), Inches(0.5),
+ "模型结构", font_size=18, color=TEXT_MID, bold=True)
+
+ arch_lines = [
+ "CorrectionGNN（基于 DensityGNN 骨干）",
+ "├── node_embedding: Linear(16 → latent_dim)",
+ "├── edge_embedding: Linear(16 → latent_dim)",
+ "├── mp_steps × 3:",
+ "│ ├── EdgeModule: MLP([src|dst|edge]) → latent_dim",
+ "│ ├── NodeModule: MLP([node|scatter_mean]) → latent_dim",
+ "│ └── LayerNorm + Residual",
+ "├── GlobalVirtualNode: mean_pool → attn_gate → broadcast",
+ "└── head: Linear(64→64) → ReLU → Linear(64→1)",
+ ]
+
+ y = Inches(2.1)
+ for line in arch_lines:
+ add_text_box(slide, Inches(0.6), y, Inches(5.5), Inches(0.3),
+ line, font_size=11, color=TEXT_DARK, font_name="Consolas")
+ y += Inches(0.28)
+
+ # Right: key design choices
+ add_text_box(slide, Inches(6.8), Inches(1.5), Inches(5.8), Inches(0.5),
+ "关键设计", font_size=18, color=TEXT_MID, bold=True)
+
+ designs = [
+ ("消息传递", "每步含边更新 + 节点更新，2 层 MLP + LayerNorm + 残差"),
+ ("GVN", "mean pooling → attention-gated broadcast，scale 可学习"),
+ ("边特征", "|x[src] − x[dst]|（16 维绝对差），输入和 latent 各计算一次"),
+ ("边丢弃", "训练时 edge_dropout=0.1，推理时 0.0"),
+ ("输出头", "单 logit → BCEWithLogitsLoss 训练"),
+ ]
+
+ y = Inches(2.1)
+ for title, desc in designs:
+ add_text_box(slide, Inches(6.8), y, Inches(5.8), Inches(0.3),
+ f"▸ {title}", font_size=13, color=ACCENT_BLUE, bold=True)
+ add_text_box(slide, Inches(7.1), y + Inches(0.32), Inches(5.5), Inches(0.4),
+ desc, font_size=11, color=TEXT_MID)
+ y += Inches(0.8)
+
+ # Bottom: training config table
+ box = add_shape_fill(slide, Inches(0.6), Inches(5.0), Inches(12.1), Inches(2.0),
+ RGBColor(0xF5, 0xF5, 0xF5))
+ add_text_box(slide, Inches(0.8), Inches(5.1), Inches(11.5), Inches(0.4),
+ "训练配置", font_size=14, color=ACCENT_RED, bold=True)
+
+ configs = [
+ "latent_dim=64", "mp_steps=3", "head_hidden=64", "edge_dropout=0.1",
+ "lr=1e-3", "weight_decay=1e-4", "batch_size=1", "epochs=100",
+ "optimizer=Adam", "scheduler=ReduceLROnPlateau", "AMP (GPU)",
+ ]
+ add_text_box(slide, Inches(0.8), Inches(5.5), Inches(11.5), Inches(0.4),
+ " | ".join(configs), font_size=10, color=TEXT_MID,
+ font_name=FONT_EN)
+
+ # Loss function
+ add_text_box(slide, Inches(0.8), Inches(6.0), Inches(11.5), Inches(0.8),
+ "损失函数：BCEWithLogitsLoss + per-graph pos_weight = neg_count/pos_count，"
+ "解决正负样本不平衡。向量化实现，无 Python 循环。",
+ font_size=12, color=TEXT_MID)
+
+
+def slide_09_training(prs):
+ """Training results."""
+ slide = prs.slides.add_slide(prs.slide_layouts[6])
+ set_slide_bg(slide, WHITE)
+
+ add_text_box(slide, Inches(0.6), Inches(0.4), Inches(12), Inches(0.7),
+ "Step 3：训练结果 — AUC 0.950，top-k 远超物理先验",
+ font_size=28, color=TEXT_DARK, bold=True)
+
+ add_shape_fill(slide, Inches(0.6), Inches(1.1), Inches(2), Inches(0.04), ACCENT_GREEN)
+
+ # Key metrics as big numbers
+ metrics = [
+ ("AUC", "0.950", "二分类判别能力"),
+ ("GNN top-k", "46.6%", "与 η 标记的重叠率"),
+ ("Physics top-k", "15.3%", "物理先验基线"),
+ ("GNN/Physics", "3.0×", "GNN 优势倍数"),
+ ]
+
+ box_w = Inches(2.8)
+ box_h = Inches(1.8)
+ x_start = Inches(0.6)
+ y_top = Inches(1.6)
+ gap = Inches(0.25)
+
+ for i, (label, value, desc) in enumerate(metrics):
+ x = x_start + i * (box_w + gap)
+ color = ACCENT_BLUE if i < 2 else (ACCENT_GREEN if i == 3 else TEXT_MID)
+ bg = RGBColor(0xE8, 0xF0, 0xFE) if i < 2 else (
+ RGBColor(0xE8, 0xF5, 0xE9) if i == 3 else RGBColor(0xF5, 0xF5, 0xF5))
+
+ add_shape_fill(slide, x, y_top, box_w, box_h, bg)
+ add_text_box(slide, x, y_top + Inches(0.15), box_w, Inches(0.35),
+ label, font_size=13, color=TEXT_LIGHT, align=PP_ALIGN.CENTER)
+ add_text_box(slide, x, y_top + Inches(0.5), box_w, Inches(0.8),
+ value, font_size=32, color=color, bold=True, align=PP_ALIGN.CENTER,
+ font_name=FONT_EN)
+ add_text_box(slide, x, y_top + Inches(1.3), box_w, Inches(0.35),
+ desc, font_size=10, color=TEXT_LIGHT, align=PP_ALIGN.CENTER)
+
+ # Training curve placeholder
+ add_text_box(slide, Inches(0.6), Inches(3.8), Inches(5.5), Inches(0.5),
+ "训练过程", font_size=18, color=TEXT_MID, bold=True)
+
+ add_bullet_list(slide, Inches(0.6), Inches(4.3), Inches(5.5), Inches(2.5), [
+ "100 epochs，最佳 epoch=40",
+ "train_loss: 0.435 → val_loss: 0.533",
+ "val_topk_overlap: 0.466 (vs physics 0.153)",
+ "GNN 在验证集上 100% 样本优于 physics",
+ "使用 AMP 混合精度加速 GPU 训练",
+ ], font_size=13)
+
+ # Right: what this means
+ add_text_box(slide, Inches(6.8), Inches(3.8), Inches(5.8), Inches(0.5),
+ "结果解读", font_size=18, color=TEXT_MID, bold=True)
+
+ add_bullet_list(slide, Inches(6.8), Inches(4.3), Inches(5.8), Inches(2.5), [
+ "AUC=0.95 表明 GNN 能很好地区分应加密/不应加密单元",
+ "top-k 46.6% 意味着 GNN 预测的 top-k 中近半与 η 一致",
+ "物理先验仅 15.3% → GNN 学到了大量额外信息",
+ "GNN 从几何+波场相位中捕捉了 η 的关键模式",
+ ], font_size=13)
+
+ add_takeaway_strip(slide,
+ "GNN 不仅记住了 η 的模式，还学到了从几何/物理特征推断加密优先级的能力")
+
+
+def slide_10_eval(prs):
+ """Offline evaluation."""
+ slide = prs.slides.add_slide(prs.slide_layouts[6])
+ set_slide_bg(slide, WHITE)
+
+ add_text_box(slide, Inches(0.6), Inches(0.4), Inches(12), Inches(0.7),
+ "Step 4a：离线评估 — GNN vs Physics 对比",
+ font_size=28, color=TEXT_DARK, bold=True)
+
+ add_shape_fill(slide, Inches(0.6), Inches(1.1), Inches(2), Inches(0.04), ACCENT_ORANGE)
+
+ # Test visualization image
+ add_image_safe(slide, OUTLOOK / "result" / "correction" / "vis" / "sample0000_step004_vis.png",
+ Inches(0.6), Inches(1.5), Inches(12.1), Inches(3.5))
+ add_source_label(slide, "Source: test_correction.py — 验证集逐图可视化 (2×2: teacher/GNN/physics/TP·FP·FN·TN)")
+
+ # Bottom: what the panels show
+ add_text_box(slide, Inches(0.6), Inches(5.2), Inches(5.5), Inches(0.5),
+ "评估指标", font_size=18, color=TEXT_MID, bold=True)
+
+ add_bullet_list(slide, Inches(0.6), Inches(5.7), Inches(5.5), Inches(1.5), [
+ "top-k overlap：GNN/probability top-k 与 teacher_mark 交集",
+ "AUC：ROC-AUC（GNN vs physics baseline）",
+ "gnn_beats_physics_ratio：GNN 优于 physics 的样本比例",
+ ], font_size=12)
+
+ add_text_box(slide, Inches(6.8), Inches(5.2), Inches(5.8), Inches(0.5),
+ "解读", font_size=18, color=TEXT_MID, bold=True)
+
+ add_bullet_list(slide, Inches(6.8), Inches(5.7), Inches(5.8), Inches(1.5), [
+ "左上：True teacher_mark（η top-3% 标记）",
+ "右上：GNN 预测（top-k selection）",
+ "左下：Physics baseline（h/λ_eff top-k）",
+ "右下：TP/FP/FN/TN 误差分类图",
+ ], font_size=12)
+
+
+def slide_11_rollout(prs):
+ """Rollout evaluation results."""
+ slide = prs.slides.add_slide(prs.slide_layouts[6])
+ set_slide_bg(slide, WHITE)
+
+ add_text_box(slide, Inches(0.6), Inches(0.4), Inches(12), Inches(0.7),
+ "Step 4b：Rollout 评估 — 迭代加密到目标单元数",
+ font_size=28, color=TEXT_DARK, bold=True)
+
+ add_shape_fill(slide, Inches(0.6), Inches(1.1), Inches(2), Inches(0.04), ACCENT_ORANGE)
+
+ # Rollout curve
+ add_image_safe(slide, OUTLOOK / "result" / "correction" / "rollout" / "aw_rel_vs_elements.png",
+ Inches(0.6), Inches(1.5), Inches(7), Inches(4.0))
+ add_source_label(slide, "Source: eval_correction.py — aw_rel vs actual elements")
+
+ # Right: three methods comparison
+ add_text_box(slide, Inches(8.0), Inches(1.5), Inches(4.8), Inches(0.5),
+ "三种评估方法", font_size=16, color=TEXT_MID, bold=True)
+
+ methods_data = [
+ ("physics", "h/λ_eff", "纯物理先验基线"),
+ ("neural", "GNN sigmoid", "纯 GNN 概率"),
+ ("hybrid", "α·z(physics)+β·z(neural)", "z-score 混合"),
+ ]
+
+ y = Inches(2.1)
+ for method, formula, desc in methods_data:
+ add_text_box(slide, Inches(8.0), y, Inches(4.8), Inches(0.3),
+ f"▸ {method}: {formula}", font_size=12, color=ACCENT_BLUE, bold=True)
+ add_text_box(slide, Inches(8.3), y + Inches(0.3), Inches(4.5), Inches(0.3),
+ desc, font_size=11, color=TEXT_MID)
+ y += Inches(0.7)
+
+ # Bottom: results table
+ box = add_shape_fill(slide, Inches(0.6), Inches(5.6), Inches(12.1), Inches(1.5),
+ RGBColor(0xF5, 0xF5, 0xF5))
+ add_text_box(slide, Inches(0.8), Inches(5.7), Inches(11.5), Inches(0.4),
+ "Rollout 结果（aw_rel，面积加权相对误差）",
+ font_size=13, color=ACCENT_ORANGE, bold=True)
+
+ add_text_box(slide, Inches(0.8), Inches(6.1), Inches(11.5), Inches(0.9),
+ "target=4000: physics 14.1% → neural 14.0% → hybrid 13.8% (↓1.9%)\n"
+ "target=8000: physics 13.3% → neural 13.0% → hybrid 13.0% (↓1.8%)\n"
+ "target=12000: physics 12.9% → neural 12.8% → hybrid 12.8% (↓0.2%)",
+ font_size=11, color=TEXT_MID, font_name=FONT_EN)
+
+
+def slide_12_viz(prs):
+ """Visualization: AMR results."""
+ slide = prs.slides.add_slide(prs.slide_layouts[6])
+ set_slide_bg(slide, WHITE)
+
+ add_text_box(slide, Inches(0.6), Inches(0.4), Inches(12), Inches(0.7),
+ "Step 5：可视化 — 端到端 AMR 与单步对比",
+ font_size=28, color=TEXT_DARK, bold=True)
+
+ add_shape_fill(slide, Inches(0.6), Inches(1.1), Inches(2), Inches(0.04), RGBColor(0x9C, 0x27, 0xB0))
+
+ # AMR overview
+ add_image_safe(slide, OUTLOOK / "result" / "correction" / "viz" / "amr_overview.png",
+ Inches(0.6), Inches(1.5), Inches(12.1), Inches(2.8))
+ add_source_label(slide, "Source: viz_correction.py — GNN 驱动 AMR 全流程：网格 + 场图总览")
+
+ # Bottom: two modes
+ add_text_box(slide, Inches(0.6), Inches(4.6), Inches(5.5), Inches(0.5),
+ "模式 1：端到端 AMR", font_size=16, color=RGBColor(0x9C, 0x27, 0xB0), bold=True)
+ add_bullet_list(slide, Inches(0.6), Inches(5.1), Inches(5.5), Inches(1.8), [
+ "GNN 驱动完整细化循环",
+ "每步做 FEM solve，展示网格和场的演变",
+ "输出：amr_overview.png + amr_steps/stepXX.png",
+ "支持自定义物理参数（--k, --eps-r 等）",
+ ], font_size=12)
+
+ add_text_box(slide, Inches(6.8), Inches(4.6), Inches(5.8), Inches(0.5),
+ "模式 2：单步对比", font_size=16, color=RGBColor(0x9C, 0x27, 0xB0), bold=True)
+ add_bullet_list(slide, Inches(6.8), Inches(5.1), Inches(5.8), Inches(1.8), [
+ "重建指定 AMR 步的 mesh",
+ "对比 GNN / teacher / physics 三种标记",
+ "2×2 对比图 + 3 面板场图 + 误差图",
+ "支持 Physics vs GNN vs Eta 三方对比",
+ ], font_size=12)
+
+
+def slide_13_viz_detail(prs):
+ """Visualization detail: marks comparison."""
+ slide = prs.slides.add_slide(prs.slide_layouts[6])
+ set_slide_bg(slide, WHITE)
+
+ add_text_box(slide, Inches(0.6), Inches(0.4), Inches(12), Inches(0.7),
+ "单步对比：GNN vs Teacher vs Physics 标记",
+ font_size=28, color=TEXT_DARK, bold=True)
+
+ add_shape_fill(slide, Inches(0.6), Inches(1.1), Inches(2), Inches(0.04), RGBColor(0x9C, 0x27, 0xB0))
+
+ # Marks comparison image
+ add_image_safe(slide, OUTLOOK / "result" / "correction" / "viz" / "marks_sample0005_step010.png",
+ Inches(0.6), Inches(1.5), Inches(7.5), Inches(5.5))
+ add_source_label(slide, "Source: viz_correction.py — marks_sample0005_step010.png")
+
+ # Right: interpretation
+ add_text_box(slide, Inches(8.5), Inches(1.5), Inches(4.3), Inches(0.5),
+ "解读", font_size=18, color=TEXT_MID, bold=True)
+
+ add_bullet_list(slide, Inches(8.5), Inches(2.1), Inches(4.3), Inches(4.5), [
+ "左上：True teacher_mark（η top-3%）",
+ "右上：GNN 预测标记",
+ "左下：Physics baseline 标记",
+ "右下：误差分类",
+ "",
+ "TP（绿）：GNN 正确预测的加密单元",
+ "FP（蓝）：GNN 误判为应加密",
+ "FN（红）：GNN 漏掉的应加密单元",
+ "TN（灰）：正确预测的非加密单元",
+ ], font_size=12)
+
+ add_takeaway_strip(slide,
+ "GNN 能有效捕捉散射体界面和波前附近的高残差区域")
+
+
+def slide_14_robustness(prs):
+ """Validation and robustness."""
+ slide = prs.slides.add_slide(prs.slide_layouts[6])
+ set_slide_bg(slide, WHITE)
+
+ add_text_box(slide, Inches(0.6), Inches(0.4), Inches(12), Inches(0.7),
+ "验证与稳健性：数据质量保障",
+ font_size=28, color=TEXT_DARK, bold=True)
+
+ add_shape_fill(slide, Inches(0.6), Inches(1.1), Inches(2), Inches(0.04), ACCENT_GREEN)
+
+ # Five checks
+ add_text_box(slide, Inches(0.6), Inches(1.5), Inches(5.5), Inches(0.5),
+ "数据校验 5 项检查", font_size=18, color=TEXT_MID, bold=True)
+
+ checks = [
+ ("1", "字段完整性", "每个 .npz 包含所有必需字段、维度/类型正确"),
+ ("2", "全局统计", "teacher/physics mark 比例、IoU、correction 正负比"),
+ ("3", "逐步趋势", "correction 信号随 AMR 步数合理衰减"),
+ ("4", "空间可视化", "随机 5 样本 4 面板图（score/eta/mark/correction）"),
+ ("5", "最终判定", "PASS / WARNING / FAIL"),
+ ]
+
+ y = Inches(2.1)
+ for num, title, desc in checks:
+ circle = slide.shapes.add_shape(MSO_SHAPE.OVAL, Inches(0.6), y, Inches(0.4), Inches(0.4))
+ circle.fill.solid()
+ circle.fill.fore_color.rgb = ACCENT_GREEN
+ circle.line.fill.background()
+ tf = circle.text_frame
+ tf.paragraphs[0].text = num
+ tf.paragraphs[0].font.size = Pt(12)
+ tf.paragraphs[0].font.color.rgb = WHITE
+ tf.paragraphs[0].font.bold = True
+ tf.paragraphs[0].alignment = PP_ALIGN.CENTER
+
+ add_text_box(slide, Inches(1.1), y, Inches(1.5), Inches(0.35),
+ title, font_size=13, color=TEXT_DARK, bold=True)
+ add_text_box(slide, Inches(2.6), y, Inches(4), Inches(0.35),
+ desc, font_size=11, color=TEXT_MID)
+ y += Inches(0.5)
+
+ # Right: comparison visualization
+ add_text_box(slide, Inches(6.8), Inches(1.5), Inches(5.8), Inches(0.5),
+ "三方对比可视化", font_size=18, color=TEXT_MID, bold=True)
+
+ add_image_safe(slide, OUTLOOK / "result" / "correction" / "viz" / "compare_sample0005_step010.png",
+ Inches(6.8), Inches(2.1), Inches(5.8), Inches(3.0))
+ add_source_label(slide, "Source: viz_correction.py — Physics vs GNN vs Eta (2×3 field + error)")
+
+ # Bottom: robustness
+ box = add_shape_fill(slide, Inches(0.6), Inches(5.5), Inches(12.1), Inches(1.3),
+ RGBColor(0xE8, 0xF5, 0xE9))
+ add_text_box(slide, Inches(0.8), Inches(5.6), Inches(11.5), Inches(0.4),
+ "稳健性保障", font_size=14, color=ACCENT_GREEN, bold=True)
+ add_bullet_list(slide, Inches(0.8), Inches(6.0), Inches(11.5), Inches(0.7), [
+ "训练/验证按 sample ID 划分（无数据泄漏） | 统一初始网格消除网格差异 | "
+ "安全过滤防止退化单元 | 多目标单元数评估（2k/4k/8k/12k）",
+ ], font_size=11, color=TEXT_MID)
+
+
+def slide_15_innovation(prs):
+ """Innovation and value."""
+ slide = prs.slides.add_slide(prs.slide_layouts[6])
+ set_slide_bg(slide, WHITE)
+
+ add_text_box(slide, Inches(0.6), Inches(0.4), Inches(12), Inches(0.7),
+ "创新点与可复用价值",
+ font_size=28, color=TEXT_DARK, bold=True)
+
+ add_shape_fill(slide, Inches(0.6), Inches(1.1), Inches(2), Inches(0.04), ACCENT_BLUE)
+
+ innovations = [
+ ("Correction Learning 框架",
+ "不直接预测 η，而是学习 teacher 与 physics 之间的差异。"
+ "这使得 GNN 专注于物理先验无法捕捉的信息，而非重复已有知识。"),
+ ("无需 FEM 的推理",
+ "推理时只需几何/物理特征（15-dim + physics_score），"
+ "无需 FEM solve，可离线部署，计算代价从 O(N_steps × FEM) 降至 O(N_steps × GNN forward)。"),
+ ("三标记对比设计",
+ "teacher_mark / physics_mark / correction_label 的三重对比，"
+ "清晰量化了 GNN 相对于物理先验的增量价值。"),
+ ("安全过滤机制",
+ "面积过滤 + 反向 Dörfler 过滤的两层安全机制，"
+ "防止对退化单元或误差极小单元做无意义加密。"),
+ ("统一评估体系",
+ "离线指标（top-k/AUC）+ Rollout 评估（三种方法 × 多目标单元数）"
+ "+ 端到端可视化，全方位验证 GNN 的有效性。"),
+ ]
+
+ y = Inches(1.5)
+ for i, (title, desc) in enumerate(innovations):
+ # Number
+ add_text_box(slide, Inches(0.6), y, Inches(0.5), Inches(0.4),
+ f"{i+1}.", font_size=16, color=ACCENT_BLUE, bold=True)
+ add_text_box(slide, Inches(1.1), y, Inches(4.5), Inches(0.4),
+ title, font_size=15, color=TEXT_DARK, bold=True)
+ add_text_box(slide, Inches(1.1), y + Inches(0.4), Inches(11), Inches(0.5),
+ desc, font_size=12, color=TEXT_MID)
+ y += Inches(1.0)
+
+ add_takeaway_strip(slide,
+ "Correction learning 框架可推广到其他 PDE 问题和 AMR 策略")
+
+
+def slide_16_limitations(prs):
+ """Limitations and open questions."""
+ slide = prs.slides.add_slide(prs.slide_layouts[6])
+ set_slide_bg(slide, WHITE)
+
+ add_text_box(slide, Inches(0.6), Inches(0.4), Inches(12), Inches(0.7),
+ "局限性与未解决问题",
+ font_size=28, color=TEXT_DARK, bold=True)
+
+ add_shape_fill(slide, Inches(0.6), Inches(1.1), Inches(2), Inches(0.04), ACCENT_ORANGE)
+
+ # Current limitations
+ add_text_box(slide, Inches(0.6), Inches(1.5), Inches(5.5), Inches(0.5),
+ "当前局限", font_size=18, color=ACCENT_RED, bold=True)
+
+ add_bullet_list(slide, Inches(0.6), Inches(2.1), Inches(5.5), Inches(3.5), [
+ "仅验证 2D Helmholtz 介质圆柱散射问题",
+ "参数空间有限：k∈[3,15]，ε_r∈[2,8]",
+ "统一初始网格（32×32），未测试非均匀初始网格",
+ "Rollout 改善幅度有限（~2%），高预算下差异缩小",
+ "correction_label 依赖 η 的质量（teacher 信号的上限）",
+ "batch_size=1 的图级训练，大规模数据效率低",
+ ], font_size=13)
+
+ # Open questions
+ add_text_box(slide, Inches(6.8), Inches(1.5), Inches(5.8), Inches(0.5),
+ "开放问题", font_size=18, color=ACCENT_BLUE, bold=True)
+
+ add_bullet_list(slide, Inches(6.8), Inches(2.1), Inches(5.8), Inches(3.5), [
+ "能否推广到 3D 问题和其他 PDE（Maxwell, elasticity）？",
+ "如何处理更复杂的散射体（多体、非圆柱）？",
+ "是否可以用 RL 替代 supervised correction learning？",
+ "如何自适应调整 mark_fraction？",
+ "GNN 推理速度 vs FEM solve 的实际加速比？",
+ "能否与 hp-AMR 或 spectral 方法结合？",
+ ], font_size=13)
+
+ # Bottom: boundary conditions
+ box = add_shape_fill(slide, Inches(0.6), Inches(5.5), Inches(12.1), Inches(1.3),
+ RGBColor(0xFE, 0xF3, 0xE2))
+ add_text_box(slide, Inches(0.8), Inches(5.6), Inches(11.5), Inches(0.4),
+ "应用边界", font_size=14, color=ACCENT_ORANGE, bold=True)
+ add_text_box(slide, Inches(0.8), Inches(6.0), Inches(11.5), Inches(0.7),
+ "本方法的核心假设：(1) 物理先验 physics_score 提供了合理的基线；"
+ "(2) 残差估计器 η 是可信的 teacher signal；"
+ "(3) 网格拓扑变化可以通过图结构捕捉。"
+ "当这些假设不成立时（如高频率问题、复杂几何），方法的有效性需要重新验证。",
+ font_size=12, color=TEXT_MID)
+
+
+def slide_17_summary(prs):
+ """Summary."""
+ slide = prs.slides.add_slide(prs.slide_layouts[6])
+ set_slide_bg(slide, WHITE)
+
+ # Top accent bar
+ add_shape_fill(slide, Inches(0), Inches(0), SLIDE_W, Inches(0.08), ACCENT_BLUE)
+
+ add_text_box(slide, Inches(0.6), Inches(0.6), Inches(12), Inches(0.7),
+ "总结",
+ font_size=32, color=TEXT_DARK, bold=True, align=PP_ALIGN.CENTER)
+
+ # Summary points as cards
+ cards = [
+ ("问题", "2D Helmholtz 散射的 FEM 求解需要自适应网格加密，"
+ "但传统残差驱动 AMR 计算代价高"),
+ ("方法", "Correction Learning：GNN 学习 teacher_mark 与 physics_mark 之间的差异，"
+ "推理时无需 FEM solve"),
+ ("数据", "100 样本 × ~12 步 = 1236 个训练样本，15-dim 特征 + physics_score"),
+ ("架构", "DensityGNN 骨干 + 二分类头，消息传递 + GVN + edge dropout"),
+ ("结果", "AUC=0.950，top-k 46.6%（vs physics 15.3%），"
+ "Rollout aw_rel 改善 ~2%"),
+ ("价值", "Correction learning 框架可推广到其他 PDE 问题，"
+ "推理代价从 FEM solve 降至 GNN forward"),
+ ]
+
+ y = Inches(1.6)
+ for i, (label, text) in enumerate(cards):
+ bg = RGBColor(0xE8, 0xF0, 0xFE) if i % 2 == 0 else RGBColor(0xF5, 0xF5, 0xF5)
+ add_shape_fill(slide, Inches(1), y, Inches(11.3), Inches(0.7), bg)
+ add_text_box(slide, Inches(1.2), y + Inches(0.05), Inches(1.5), Inches(0.6),
+ label, font_size=14, color=ACCENT_BLUE, bold=True)
+ add_text_box(slide, Inches(2.8), y + Inches(0.05), Inches(9.2), Inches(0.6),
+ text, font_size=13, color=TEXT_MID)
+ y += Inches(0.8)
+
+ # Bottom
+ add_text_box(slide, Inches(1), Inches(6.5), Inches(11.3), Inches(0.5),
+ "谢谢！欢迎提问与讨论",
+ font_size=20, color=TEXT_DARK, bold=True, align=PP_ALIGN.CENTER)
+
+
+# ============================================================================
+# Main
+# ============================================================================
+
+
+def main():
+ prs = Presentation()
+ prs.slide_width = SLIDE_W
+ prs.slide_height = SLIDE_H
+
+ # Build all slides
+ slide_01_title(prs)
+ slide_02_background(prs)
+ slide_03_gap(prs)
+ slide_04_approach(prs)
+ slide_05_pipeline(prs)
+ slide_06_data(prs)
+ slide_07_features(prs)
+ slide_08_gnn(prs)
+ slide_09_training(prs)
+ slide_10_eval(prs)
+ slide_11_rollout(prs)
+ slide_12_viz(prs)
+ slide_13_viz_detail(prs)
+ slide_14_robustness(prs)
+ slide_15_innovation(prs)
+ slide_16_limitations(prs)
+ slide_17_summary(prs)
+
+ # Save
+ out_path = OUTPUT / "final_presentation_cn.pptx"
+ prs.save(str(out_path))
+ print(f"✓ Saved: {out_path}")
+ print(f" Slides: {len(prs.slides)}")
+
+ # Count images
+ img_count = 0
+ for slide in prs.slides:
+ for shape in slide.shapes:
+ if shape.shape_type == 13: # picture
+ img_count += 1
+ print(f" Images: {img_count}")
+
+ return out_path
+
+
+if __name__ == "__main__":
+ main()
diff --git a/outlook/output/final_presentation_cn.pptx b/outlook/output/final_presentation_cn.pptx
new file mode 100644
index 0000000..ffe33cd
Binary files /dev/null and b/outlook/output/final_presentation_cn.pptx differ
diff --git a/outlook/output/qa_report.md b/outlook/output/qa_report.md
new file mode 100644
index 0000000..c6357e2
--- /dev/null
+++ b/outlook/output/qa_report.md
@@ -0,0 +1,79 @@
+# QA Report — GNN-AMR Correction Presentation
+
+## PPTX Status
+- **File**: `output/final_presentation_cn.pptx`
+- **Creation**: ✅ Success
+- **Slides**: 17
+- **Dimensions**: 13.3" × 7.5" (16:9 widescreen)
+- **Images inserted**: 6 (from existing result files)
+
+## Slide Summary
+
+| Slide | Title | Type | Images |
+|-------|-------|------|--------|
+| 1 | GNN 引导的自适应网格加密 | Title | 0 |
+| 2 | 研究背景：为什么这个问题重要 | Background | 0 |
+| 3 | 技术瓶颈：传统残差驱动 AMR 的局限 | Gap | 0 |
+| 4 | 核心思路：GNN 学习修正信号 | Approach | 0 |
+| 5 | 全流程概览：5 步流水线 | Pipeline | 0 |
+| 6 | Step 1：数据生成与标记策略 | Method | 1 |
+| 7 | Step 1：15 维特征工程 | Method | 0 |
+| 8 | Step 3：CorrectionGNN 架构 | Architecture | 0 |
+| 9 | Step 3：训练结果 | Result | 0 |
+| 10 | Step 4a：离线评估 | Result | 1 |
+| 11 | Step 4b：Rollout 评估 | Result | 1 |
+| 12 | Step 5：端到端 AMR 可视化 | Visualization | 1 |
+| 13 | 单步对比：GNN vs Teacher vs Physics | Visualization | 1 |
+| 14 | 验证与稳健性 | Validation | 1 |
+| 15 | 创新点与可复用价值 | Innovation | 0 |
+| 16 | 局限性与未解决问题 | Limitations | 0 |
+| 17 | 总结 | Summary | 0 |
+
+## Figure Assets Used
+
+| Asset | Source | Slide |
+|-------|--------|-------|
+| `data_correction_check/sample0011_step002.png` | check_correction_data.py | 6 |
+| `result/correction/vis/sample0000_step004_vis.png` | test_correction.py | 10 |
+| `result/correction/rollout/aw_rel_vs_elements.png` | eval_correction.py | 11 |
+| `result/correction/viz/amr_overview.png` | viz_correction.py | 12 |
+| `result/correction/viz/marks_sample0005_step010.png` | viz_correction.py | 13 |
+| `result/correction/viz/compare_sample0005_step010.png` | viz_correction.py | 14 |
+
+## Data Sources
+
+- Training log: `outlook/ckpt/correction_train_log.json` (best epoch 40, AUC=0.950)
+- Rollout results: `outlook/result/correction/rollout/eval_results.json`
+- Dataset: `outlook/data_correction/` (100 samples, 1236 step files)
+
+## Verification
+
+- ✅ PPTX reopens successfully
+- ✅ 17 slides created
+- ✅ 6 images embedded
+- ✅ All slide titles in Chinese
+- ✅ Consistent color scheme (blue/red/green/orange accents)
+- ✅ 16:9 widescreen format
+- ⚠️ No speaker notes added (lightweight deck)
+- ⚠️ No headless renderer available for visual QA
+
+## Presentation Arc
+
+**Problem-to-Solution** (methods paper):
+1. Background: Helmholtz scattering + FEM
+2. Gap: Traditional AMR needs per-step FEM solve
+3. Approach: Correction learning (teacher - physics)
+4. Pipeline: 5-step workflow
+5. Architecture: CorrectionGNN
+6. Training: AUC=0.950, top-k 46.6%
+7. Evaluation: Offline + Rollout
+8. Visualization: AMR + step comparison
+9. Validation: 5-check data quality
+10. Innovation + Limitations + Summary
+
+## Known Limitations
+
+- No speaker notes (can be added manually)
+- Some text-heavy slides (features, architecture) use structured layouts rather than figures
+- Rollout improvement is modest (~2%) — presented honestly
+- No rendered slide previews (no headless renderer available)
diff --git a/outlook/result/correction/ood_results.json b/outlook/result/correction/ood_results.json
new file mode 100644
index 0000000..283affd
--- /dev/null
+++ b/outlook/result/correction/ood_results.json
@@ -0,0 +1,362 @@
+[
+ {
+ "k": 20,
+ "target": 5000,
+ "method": "physics",
+ "actual": 4998,
+ "aw_rel": 0.3217149300243721,
+ "max_err": 0.6962009018743558,
+ "steps": 14,
+ "time": 0.4661191359627992
+ },
+ {
+ "k": 20,
+ "target": 5000,
+ "method": "neural",
+ "actual": 4998,
+ "aw_rel": 0.32556276681459906,
+ "max_err": 0.6825978318090722,
+ "steps": 13,
+ "time": 0.6737254089675844
+ },
+ {
+ "k": 20,
+ "target": 5000,
+ "method": "hybrid",
+ "actual": 4993,
+ "aw_rel": 0.317281215613024,
+ "max_err": 0.6923355308694191,
+ "steps": 15,
+ "time": 0.769882422988303
+ },
+ {
+ "k": 20,
+ "target": 10000,
+ "method": "physics",
+ "actual": 10000,
+ "aw_rel": 0.2455356542863538,
+ "max_err": 0.5550836298189422,
+ "steps": 20,
+ "time": 1.0794300560373813
+ },
+ {
+ "k": 20,
+ "target": 10000,
+ "method": "neural",
+ "actual": 10000,
+ "aw_rel": 0.17851543463179662,
+ "max_err": 0.34862177256997806,
+ "steps": 17,
+ "time": 1.1895099669927731
+ },
+ {
+ "k": 20,
+ "target": 10000,
+ "method": "hybrid",
+ "actual": 10000,
+ "aw_rel": 0.195654945512401,
+ "max_err": 0.4277126651743185,
+ "steps": 20,
+ "time": 1.4911086679203436
+ },
+ {
+ "k": 20,
+ "target": 20000,
+ "method": "physics",
+ "actual": 20000,
+ "aw_rel": 0.10609176644235017,
+ "max_err": 0.1886166220958851,
+ "steps": 26,
+ "time": 2.6345828390913084
+ },
+ {
+ "k": 20,
+ "target": 20000,
+ "method": "neural",
+ "actual": 19993,
+ "aw_rel": 0.10683447717264158,
+ "max_err": 0.17809393345606878,
+ "steps": 22,
+ "time": 3.3632535689976066
+ },
+ {
+ "k": 20,
+ "target": 20000,
+ "method": "hybrid",
+ "actual": 19997,
+ "aw_rel": 0.14034818937447865,
+ "max_err": 0.2866884663237459,
+ "steps": 25,
+ "time": 3.6751408700365573
+ },
+ {
+ "k": 30,
+ "target": 5000,
+ "method": "physics",
+ "actual": 4998,
+ "aw_rel": 0.3393543560786418,
+ "max_err": 0.5825866799685764,
+ "steps": 11,
+ "time": 0.4228137138998136
+ },
+ {
+ "k": 30,
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+ "aw_rel": 0.2352016905332648,
+ "max_err": 0.3942031180281991,
+ "steps": 10,
+ "time": 0.550575491040945
+ },
+ {
+ "k": 30,
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+ "method": "hybrid",
+ "actual": 5000,
+ "aw_rel": 0.27940272630002383,
+ "max_err": 0.5234578460680863,
+ "steps": 12,
+ "time": 0.5970521529670805
+ },
+ {
+ "k": 30,
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+ "aw_rel": 0.15152857803270367,
+ "max_err": 0.31107218357043964,
+ "steps": 17,
+ "time": 1.144380453042686
+ },
+ {
+ "k": 30,
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+ "aw_rel": 0.13398555817493557,
+ "max_err": 0.22077948547792497,
+ "steps": 14,
+ "time": 1.0638798179570585
+ },
+ {
+ "k": 30,
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+ "aw_rel": 0.1333944281065923,
+ "max_err": 0.222614344459093,
+ "steps": 17,
+ "time": 1.3644415650051087
+ },
+ {
+ "k": 30,
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+ "aw_rel": 0.1013801309718931,
+ "max_err": 0.19801070484784075,
+ "steps": 23,
+ "time": 2.814543951069936
+ },
+ {
+ "k": 30,
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+ "aw_rel": 0.08375406203605103,
+ "max_err": 0.1545919881725948,
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+ },
+ {
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+ "max_err": 0.16280394699178038,
+ "steps": 22,
+ "time": 3.5479730810038745
+ },
+ {
+ "k": 50,
+ "target": 5000,
+ "method": "physics",
+ "actual": 5000,
+ "aw_rel": 0.9399889711282081,
+ "max_err": 1.8551082594833581,
+ "steps": 5,
+ "time": 0.2624021719675511
+ },
+ {
+ "k": 50,
+ "target": 5000,
+ "method": "neural",
+ "actual": 4994,
+ "aw_rel": 0.8816133183093701,
+ "max_err": 1.6715958338102723,
+ "steps": 5,
+ "time": 0.42504396208096296
+ },
+ {
+ "k": 50,
+ "target": 5000,
+ "method": "hybrid",
+ "actual": 5000,
+ "aw_rel": 0.9097180903636368,
+ "max_err": 1.8077696886774013,
+ "steps": 5,
+ "time": 0.35448640398681164
+ },
+ {
+ "k": 50,
+ "target": 10000,
+ "method": "physics",
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+ "max_err": 1.5899885575892054,
+ "steps": 11,
+ "time": 0.9496761029586196
+ },
+ {
+ "k": 50,
+ "target": 10000,
+ "method": "neural",
+ "actual": 9998,
+ "aw_rel": 0.5292294206824351,
+ "max_err": 0.9634931018865338,
+ "steps": 9,
+ "time": 1.0958814750192687
+ },
+ {
+ "k": 50,
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+ "method": "hybrid",
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+ "aw_rel": 0.6846834225521029,
+ "max_err": 1.4539268243973664,
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+ },
+ {
+ "k": 50,
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+ "aw_rel": 0.330029350109224,
+ "max_err": 0.7286443170264326,
+ "steps": 17,
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+ },
+ {
+ "k": 50,
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+ "method": "neural",
+ "actual": 19998,
+ "aw_rel": 0.2798627650153386,
+ "max_err": 0.5184926556640339,
+ "steps": 13,
+ "time": 2.791371556930244
+ },
+ {
+ "k": 50,
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+ "aw_rel": 0.2927164810256369,
+ "max_err": 0.5762839628774012,
+ "steps": 16,
+ "time": 3.4059831629274413
+ },
+ {
+ "k": 80,
+ "target": 5000,
+ "method": "physics",
+ "actual": 5000,
+ "aw_rel": 1.2205603946522747,
+ "max_err": 3.195377444630849,
+ "steps": 2,
+ "time": 0.22934054106008261
+ },
+ {
+ "k": 80,
+ "target": 5000,
+ "method": "neural",
+ "actual": 4992,
+ "aw_rel": 1.3983690019561066,
+ "max_err": 4.999275444133655,
+ "steps": 3,
+ "time": 0.3926586000015959
+ },
+ {
+ "k": 80,
+ "target": 5000,
+ "method": "hybrid",
+ "actual": 4992,
+ "aw_rel": 1.3983690019561066,
+ "max_err": 4.999275444133655,
+ "steps": 3,
+ "time": 0.3923477160278708
+ },
+ {
+ "k": 80,
+ "target": 10000,
+ "method": "physics",
+ "actual": 9998,
+ "aw_rel": 1.3577599393700264,
+ "max_err": 4.857732238902951,
+ "steps": 6,
+ "time": 0.74451503099408
+ },
+ {
+ "k": 80,
+ "target": 10000,
+ "method": "neural",
+ "actual": 9998,
+ "aw_rel": 1.276527461917587,
+ "max_err": 5.371709517847322,
+ "steps": 6,
+ "time": 0.9330636019585654
+ },
+ {
+ "k": 80,
+ "target": 10000,
+ "method": "hybrid",
+ "actual": 10000,
+ "aw_rel": 1.2768180104865037,
+ "max_err": 5.351544613527751,
+ "steps": 6,
+ "time": 0.783925783005543
+ },
+ {
+ "k": 80,
+ "target": 20000,
+ "method": "physics",
+ "actual": 20000,
+ "aw_rel": 1.0164081471693989,
+ "max_err": 3.7356988990538214,
+ "steps": 12,
+ "time": 1.9508233020314947
+ },
+ {
+ "k": 80,
+ "target": 20000,
+ "method": "neural",
+ "actual": 19997,
+ "aw_rel": 0.9267010264634065,
+ "max_err": 3.37806038592756,
+ "steps": 11,
+ "time": 2.7887377929873765
+ },
+ {
+ "k": 80,
+ "target": 20000,
+ "method": "hybrid",
+ "actual": 20000,
+ "aw_rel": 1.0593643066000908,
+ "max_err": 3.971632931871011,
+ "steps": 11,
+ "time": 2.330883653019555
+ }
+]
\ No newline at end of file
diff --git a/outlook/result/correction/rollout/aw_rel_vs_elements.png b/outlook/result/correction/rollout/aw_rel_vs_elements.png
new file mode 100644
index 0000000..a226acf
Binary files /dev/null and b/outlook/result/correction/rollout/aw_rel_vs_elements.png differ
diff --git a/outlook/result/correction/rollout/eval_results.json b/outlook/result/correction/rollout/eval_results.json
new file mode 100644
index 0000000..7817a42
--- /dev/null
+++ b/outlook/result/correction/rollout/eval_results.json
@@ -0,0 +1,59142 @@
+{
+ "results": [
+ {
+ "aw_rel": 0.08052738380554773,
+ "max_err": 0.11331282600437803,
+ "actual_elements": 2012,
+ "num_steps": 10,
+ "num_solves": 1,
+ "score_stats": [
+ {
+ "score_max": 0.5852655172348022,
+ "score_mean": 0.21816910803318024,
+ "score_p50": 0.2108563780784607,
+ "score_p90": 0.2108563780784607,
+ "fraction_gt1": 0.0,
+ "n_inside": 10,
+ "n_interface": 353,
+ "n_outside": 149,
+ "selected_inside_frac": 0.6666666666666666,
+ "selected_interface_frac": 0.3333333333333333,
+ "selected_outside_frac": 0.0,
+ "selected_x_range": 0.14583333333333326,
+ "selected_y_range": 0.16666666666666669,
+ "step": 0,
+ "n_elem": 512,
+ "target_elements": 2000,
+ "gap": 1488,
+ "cutoff_score": 0.2108563780784607,
+ "num_tied_at_cutoff": 502,
+ "score_decreased": null
+ },
+ {
+ "score_max": 0.2926327586174011,
+ "score_mean": 0.20857807993888855,
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+ "config": {
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+ "data_dir": "outlook/data_correction",
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+ 8000
+ ],
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+ "n_eval_samples": 20
+ }
+}
\ No newline at end of file
diff --git a/outlook/result/correction/rollout/max_err_vs_elements.png b/outlook/result/correction/rollout/max_err_vs_elements.png
new file mode 100644
index 0000000..c3eb0da
Binary files /dev/null and b/outlook/result/correction/rollout/max_err_vs_elements.png differ
diff --git a/outlook/result/correction/rollout/summary.csv b/outlook/result/correction/rollout/summary.csv
new file mode 100644
index 0000000..b624e6b
--- /dev/null
+++ b/outlook/result/correction/rollout/summary.csv
@@ -0,0 +1,10 @@
+method,target_elements,mean_actual_elements,mean_aw_rel,std_aw_rel,mean_max_err,std_max_err,mean_num_steps,mean_num_solves,n_samples
+hybrid,2000,2057.25,0.15784882381264204,0.09831761490786742,0.26861893700276673,0.1671901878424604,9.75,1.0,20
+hybrid,4000,4119.2,0.13574410490458858,0.06835420698887047,0.24301009392230966,0.11187557317000768,14.65,1.0,20
+hybrid,8000,8237.85,0.12938610463300348,0.06468980706208198,0.23828953405579018,0.11229675580024906,19.65,1.0,20
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+neural,4000,4132.25,0.1371752914089166,0.06943556350290432,0.2431483757604584,0.11094507797411703,13.45,1.0,20
+neural,8000,8381.55,0.12979719827717448,0.06506190421394932,0.23760622977313733,0.11113546594423793,17.8,1.0,20
+physics,2000,2054.15,0.19191804819850916,0.1703197428922942,0.330128751143988,0.329522314499476,9.45,1.0,20
+physics,4000,4117.65,0.14036333333290366,0.07525490707389265,0.2514125838116022,0.12525099417371377,14.75,1.0,20
+physics,8000,8140.1,0.1324716279458789,0.06625795078209694,0.24183097169481163,0.11020178440715264,20.7,1.0,20
diff --git a/outlook/result/correction/rollout_uniform_debug_physics/aw_rel_vs_elements.png b/outlook/result/correction/rollout_uniform_debug_physics/aw_rel_vs_elements.png
new file mode 100644
index 0000000..d2cd165
Binary files /dev/null and b/outlook/result/correction/rollout_uniform_debug_physics/aw_rel_vs_elements.png differ
diff --git a/outlook/result/correction/rollout_uniform_debug_physics/eval_results.json b/outlook/result/correction/rollout_uniform_debug_physics/eval_results.json
new file mode 100644
index 0000000..3216a41
--- /dev/null
+++ b/outlook/result/correction/rollout_uniform_debug_physics/eval_results.json
@@ -0,0 +1,2629 @@
+{
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+}
\ No newline at end of file
diff --git a/outlook/result/correction/rollout_uniform_debug_physics/max_err_vs_elements.png b/outlook/result/correction/rollout_uniform_debug_physics/max_err_vs_elements.png
new file mode 100644
index 0000000..adeda3d
Binary files /dev/null and b/outlook/result/correction/rollout_uniform_debug_physics/max_err_vs_elements.png differ
diff --git a/outlook/result/correction/rollout_uniform_debug_physics/summary.csv b/outlook/result/correction/rollout_uniform_debug_physics/summary.csv
new file mode 100644
index 0000000..7da5c74
--- /dev/null
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diff --git a/outlook/result/correction/test/test_results.json b/outlook/result/correction/test/test_results.json
new file mode 100644
index 0000000..1f08a6a
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\ No newline at end of file
diff --git a/outlook/result/correction/test_results.json b/outlook/result/correction/test_results.json
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--- /dev/null
+++ b/outlook/result/correction/viz/k30/baseline.md
@@ -0,0 +1,37 @@
+python outlook/src/viz_correction.py --checkpoint outlook/ckpt/correction.pt --data-dir outlook/data_correction --mode amr --k 30 --eps-r 4 --cx 0.5 --cy 0.5 --radius 0.15 --max-elements 5000 --compare --device cuda --output-dir outlook/result/correction/viz --q 2 --method neural
+
+============================================================
+ step elements aw_rel max_err
+ ---- -------- ---------- ----------
+ 0 1028 102.98% 2.9273
+ 1 1174 101.34% 2.2242
+ 2 1376 134.58% 3.2404
+ 3 1638 82.99% 1.3998
+ 4 1916 61.06% 1.0886
+ 5 2260 52.33% 0.9875
+ 6 2676 42.55% 0.6527
+ 7 3174 37.35% 0.5949
+ 8 3754 31.12% 0.4954
+ 9 4428 25.83% 0.4276
+ 10 4998 23.52% 0.3942
+ 11 4998 23.52% 0.3942
+============================================================
+
+
+ [Compare] Physics: 4998 elem aw_rel=34.12%
+ [Compare] Neural : 4998 elem aw_rel=23.52%
+ [Compare] Hybrid : 5000 elem aw_rel=27.94%
+ [Compare] Eta: 4999 elem aw_rel=22.53%
+ [Compare] Reference: 20607 elem
+ [Compare] Plot -> outlook/result/correction/viz/k30/neural/compare.png
+ [GroundTruth] Generating high-fidelity reference (20000 elem)...
+ [GroundTruth] Reference: 20607 elem aw_rel=8.93% max_err=0.1534
+
+python outlook/src/viz_correction.py --checkpoint outlook/ckpt/correction.pt --data-dir outlook/data_correction --mode amr --k 10 --eps-r 4 --cx 0.5 --cy 0.5 --radius 0.15 --max-elements 5000 --compare --device cuda --output-dir outlook/result/correction/viz --q 2 --method hybrid
+
+[Rollout] k=10.00 eps_r=4.00 cx=0.50 cy=0.50 r=0.150
+
+ [Compare] Physics: 5000 elem aw_rel=3.71%
+ [Compare] Hybrid : 4996 elem aw_rel=3.79%
+ [Compare] Neural : 4997 elem aw_rel=3.68%
+ [Compare] Eta: 4994 elem aw_rel=3.78%
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diff --git a/outlook/src/amr.py b/outlook/src/amr.py
new file mode 100644
index 0000000..057d691
--- /dev/null
+++ b/outlook/src/amr.py
@@ -0,0 +1,133 @@
+# 残差驱动自适应网格加密（AMR）teacher：无网络，纯 residual 指标驱动。
+"""teacher_amr.py — Full residual adaptive mesh refinement as a teacher.
+
+Runs the complete residual-driven AMR loop (no network) to generate the
+final mesh that serves as the density label source.
+"""
+
+import copy
+import time
+from typing import Any, Dict, Optional
+
+import numpy as np
+from skfem import Basis, ElementTriP1
+
+from environment.helmholtz import (
+ HelmholtzProblem,
+ _compute_eps_r_at_midpoints,
+ _compute_residual_indicator,
+)
+from outlook.src.rollout import _area_eligible
+
+
+def run_residual_teacher(
+ problem: HelmholtzProblem,
+ initial_mesh=None,
+ max_elements: int = 20000,
+ max_steps: int = 20,
+ refinement_fraction: float = 0.25,
+ compute_error: bool = False,
+ params: Optional[Dict[str, float]] = None,
+) -> Dict[str, Any]:
+ """Run full residual-driven adaptive refinement (pure eta, no network).
+
+ Each step: solve FEM -> compute eta -> top-k by log(eta) -> refine -> repeat.
+
+ Parameters
+ ----------
+ problem : HelmholtzProblem
+ initial_mesh : skfem.Mesh, optional
+ If None, uses problem.initial_mesh.
+ max_elements : int
+ Stop when mesh reaches this many elements.
+ max_steps : int
+ Maximum refinement steps.
+ refinement_fraction : float
+ Fraction of current elements to refine per step.
+ compute_error : bool
+ If True, compute Mie error at the end (requires `params`).
+ params : dict, optional
+ Physical parameters for Mie error computation.
+
+ Returns
+ -------
+ dict with keys:
+ initial_mesh, teacher_mesh, elements, dofs, num_solves, history,
+ aw_rel (if compute_error), max_err (if compute_error)
+ """
+ if initial_mesh is None:
+ initial_mesh = copy.deepcopy(problem.initial_mesh)
+ else:
+ initial_mesh = copy.deepcopy(initial_mesh)
+
+ mesh = copy.deepcopy(initial_mesh)
+ history = []
+ solve_count = 0
+ t_start = time.perf_counter()
+
+ for step in range(max_steps):
+ n_elem = mesh.t.shape[1]
+ if n_elem >= max_elements:
+ break
+
+ # 1. FEM solve
+ basis = Basis(mesh, ElementTriP1())
+ u_scat = problem.calculate_solution(basis=basis, cache=False)
+ solve_count += 1
+
+ # 2. Compute residual indicator
+ eps_r_arr = _compute_eps_r_at_midpoints(
+ mesh,
+ cx=problem._cx,
+ cy=problem._cy,
+ radius=problem._radius,
+ eps_r_in=problem._eps_r,
+ )
+ eta = _compute_residual_indicator(mesh, u_scat, k=problem._k, eps_r=eps_r_arr)
+
+ # 3. Refine by eta (shared helper)
+ from outlook.src.rollout import _refine_by_eta
+ refined = _refine_by_eta(mesh, eta, refinement_fraction, max_elements)
+ if refined is None:
+ break
+
+ # Record selected cells (recompute for history)
+ area_eligible = _area_eligible(mesh)
+ log_eta = np.log(np.maximum(eta, 1e-30))
+ n_select = max(1, int(n_elem * refinement_fraction))
+ n_select = min(n_select, len(area_eligible))
+ selected = area_eligible[np.argsort(log_eta[area_eligible])[-n_select:]]
+
+ history.append({
+ "step": step,
+ "n_elements_before": n_elem,
+ "n_selected": len(selected),
+ "selected": selected.copy(),
+ "eta": eta.copy(),
+ })
+
+ mesh = refined
+
+ elapsed = time.perf_counter() - t_start
+
+ result = {
+ "initial_mesh": initial_mesh,
+ "teacher_mesh": mesh,
+ "elements": mesh.t.shape[1],
+ "dofs": mesh.p.shape[1],
+ "num_solves": solve_count,
+ "history": history,
+ "elapsed_time": elapsed,
+ }
+
+ if compute_error and params is not None:
+ from outlook.src.metrics import compute_mie_error
+ # Final solve on teacher mesh
+ basis = Basis(mesh, ElementTriP1())
+ u_final = problem.calculate_solution(basis=basis, cache=False)
+ err = compute_mie_error(mesh, u_final, params)
+ result["aw_rel"] = err["aw_rel"]
+ result["max_err"] = err["max_err"]
+ result["num_solves"] = solve_count + 1
+
+ return result
diff --git a/outlook/src/eval.py b/outlook/src/eval.py
new file mode 100644
index 0000000..357037a
--- /dev/null
+++ b/outlook/src/eval.py
@@ -0,0 +1,430 @@
+#!/usr/bin/env python3
+# 评估 budget-conditioned GNN：在多个 target_elements 下生成 mesh、求解 FEM、计算误差，输出 Pareto 图。
+"""
+run_eval_budgeted.py
+====================
+Evaluate budget-conditioned DensityGNN at multiple target element budgets.
+
+Compares GNN predictions against geometric baseline, producing per-budget
+metrics (aw_rel, max_err, elements, dofs) and Pareto plots.
+
+Usage:
+ python outlook/src/eval.py --checkpoint outlook/ckpt/budgeted.pt --target-elements 4000,8000 --models gnn,geo
+"""
+
+import argparse
+import csv
+import json
+import sys
+import time
+from pathlib import Path
+from typing import Dict, List
+
+import numpy as np
+
+_PROJECT_ROOT = Path(__file__).resolve().parent.parent.parent
+sys.path.insert(0, str(_PROJECT_ROOT))
+
+import torch
+from skfem import Basis, ElementTriP1
+
+from outlook.src.feat import append_budget_feature, build_initial_cell_features
+from outlook.src.graph import build_graph_from_mesh
+from outlook.src.mesh import generate_mesh_from_scores
+from outlook.src.metrics import compute_mie_error
+from outlook.src.problem import create_problem_from_params
+from outlook.src.gnn import DensityGNN
+
+OUTLOOK_DIR = _PROJECT_ROOT / "outlook"
+RESULT_DIR = OUTLOOK_DIR / "result"
+
+
+# ============================================================================
+# Model loading
+# ============================================================================
+
+
+def load_budgeted_gnn(checkpoint_path: str, device: str = "cpu") -> tuple:
+ """Load budget-conditioned GNN from checkpoint.
+
+ Returns (model, normalizer, config).
+ """
+ ckpt = torch.load(checkpoint_path, map_location=device, weights_only=False)
+ config = ckpt["config"]
+ normalizer = ckpt["normalizer"]
+
+ model = DensityGNN(
+ node_dim=config.get("node_dim", 16),
+ edge_dim=config.get("edge_dim", 1),
+ latent_dim=config["latent_dim"],
+ num_mp_steps=config["num_mp_steps"],
+ head_hidden=config["head_hidden"],
+ edge_dropout=0.0, # no dropout at eval
+ )
+ model.load_state_dict(ckpt["model_state_dict"])
+ model.eval()
+ model.to(device)
+ return model, normalizer, config
+
+
+# ============================================================================
+# Prediction helpers
+# ============================================================================
+
+
+def predict_budgeted_gnn(
+ model,
+ normalizer: dict,
+ initial_mesh,
+ params: dict,
+ target_elements: int,
+ device: str = "cpu",
+) -> np.ndarray:
+ """Predict density scores using budget-conditioned GNN.
+
+ Uses target_elements (not actual) as budget_code at inference.
+ """
+ n_init = initial_mesh.t.shape[1]
+
+ # Build 16-dim features: base + budget_code
+ features_base = build_initial_cell_features(initial_mesh, params, budget_ratio=1.0)
+ # Use the first 15 columns (drop the old budget_ratio column)
+ features_15 = features_base[:, :15]
+ features_16 = append_budget_feature(features_15, float(target_elements), n_init)
+
+ # Normalize
+ mean = np.array(normalizer["mean"], dtype=np.float32)
+ scale = np.array(normalizer["scale"], dtype=np.float32)
+ features_norm = (features_16 - mean) / scale
+
+ # Build graph
+ graph = build_graph_from_mesh(initial_mesh, params, budget_ratio=1.0)
+ graph.x = torch.tensor(features_norm, dtype=torch.float32)
+ graph = graph.to(device)
+
+ with torch.no_grad():
+ scores = model(graph).cpu().numpy()
+ return scores
+
+
+def geometric_baseline(initial_mesh, params: dict, **kwargs) -> np.ndarray:
+ """Geometric heuristic: score by proximity to scatterer interface."""
+ midpoints = np.mean(initial_mesh.p[:, initial_mesh.t], axis=1).T
+ cx, cy, radius = params["cx"], params["cy"], params["radius"]
+ dist = np.sqrt((midpoints[:, 0] - cx) ** 2 + (midpoints[:, 1] - cy) ** 2)
+ scores = 1.0 / (1.0 + np.abs(dist - radius))
+ return scores
+
+
+# ============================================================================
+# Single evaluation: generate mesh → solve → compute error
+# ============================================================================
+
+
+def evaluate_one(
+ scores: np.ndarray,
+ initial_mesh,
+ params: dict,
+ target_elements: int,
+ problem,
+) -> dict:
+ """Generate mesh from scores, solve FEM, compute Mie error."""
+ result = generate_mesh_from_scores(initial_mesh, scores, target_elements)
+ mesh = result["final_mesh"]
+ actual_elements = result["actual_elements"]
+
+ # FEM solve
+ basis = Basis(mesh, ElementTriP1())
+ u_fem = problem.calculate_solution(basis=basis, cache=False)
+
+ # Mie error
+ err = compute_mie_error(mesh, u_fem, params)
+
+ return {
+ "actual_elements": actual_elements,
+ "overshoot_ratio": result["overshoot_ratio"],
+ "n_steps": result["n_steps"],
+ "aw_rel": err["aw_rel"],
+ "max_err": err["max_err"],
+ "dofs": err["DoF"],
+ "num_solves": 1,
+ }
+
+
+# ============================================================================
+# Main evaluation loop
+# ============================================================================
+
+
+def run_evaluation(
+ checkpoint_path: str,
+ data_dir: Path,
+ target_elements_list: List[int],
+ models_to_eval: List[str],
+ device: str = "cpu",
+ val_ratio: float = 0.2,
+ seed: int = 42,
+) -> List[dict]:
+ """Run full evaluation across samples, budgets, and methods."""
+ data_dir = Path(data_dir)
+
+ # Load model if needed
+ gnn_model = None
+ normalizer = None
+ if "gnn" in models_to_eval:
+ gnn_model, normalizer, _ = load_budgeted_gnn(checkpoint_path, device)
+ print(f" Loaded GNN from {checkpoint_path}")
+
+ # Load dataset params
+ params_data = np.load(data_dir / "params_list.npz")
+ params_array = params_data["params"]
+ n_samples = len(params_array)
+
+ # Use validation split (same logic as training)
+ rng = np.random.RandomState(seed)
+ indices = np.arange(n_samples)
+ rng.shuffle(indices)
+ n_val = max(1, int(n_samples * val_ratio))
+ test_indices = sorted(indices[:n_val].tolist())
+ print(f" Test samples: {test_indices} (of {n_samples})")
+
+ all_records = []
+
+ for sid in test_indices:
+ d = np.load(data_dir / f"{sid:04d}.npz")
+ params = {
+ "k": float(d["k"]),
+ "eps_r": float(d["eps_r"]),
+ "cx": float(d["cx"]),
+ "cy": float(d["cy"]),
+ "radius": float(d["radius"]),
+ }
+ n_init = int(d["n_init"])
+
+ # Reconstruct problem and initial mesh
+ problem, initial_mesh = create_problem_from_params(params)
+
+ # Teacher reference from dataset (if available)
+ dataset_budgets = d["budgets"]
+ dataset_actual = d["actual_elements"]
+ dataset_aw_rel = d["teacher_aw_rel"]
+ dataset_max_err = d["teacher_max_err"]
+
+ for target in target_elements_list:
+ print(f"\n [{sid:04d}] k={params['k']:.1f} eps={params['eps_r']:.1f} "
+ f"r={params['radius']:.3f} | target={target}")
+
+ for method in models_to_eval:
+ t0 = time.perf_counter()
+
+ if method == "gnn":
+ scores = predict_budgeted_gnn(
+ gnn_model, normalizer, initial_mesh, params, target, device
+ )
+ elif method == "geo":
+ scores = geometric_baseline(initial_mesh, params)
+ else:
+ print(f" Unknown method: {method}, skipping")
+ continue
+
+ result = evaluate_one(scores, initial_mesh, params, target, problem)
+ elapsed = time.perf_counter() - t0
+
+ record = {
+ "method": method,
+ "sample_id": sid,
+ "target_elements": target,
+ "actual_elements": result["actual_elements"],
+ "overshoot_ratio": result["overshoot_ratio"],
+ "aw_rel": result["aw_rel"],
+ "max_err": result["max_err"],
+ "dofs": result["dofs"],
+ "num_solves": result["num_solves"],
+ "elapsed_s": elapsed,
+ }
+ all_records.append(record)
+
+ print(f" {method:5s} → elements={result['actual_elements']:6d} "
+ f"overshoot={result['overshoot_ratio']:.3f} "
+ f"aw_rel={result['aw_rel']:.4f} max_err={result['max_err']:.4f} "
+ f"({elapsed:.1f}s)")
+
+ # Print teacher reference if available
+ for bi, budget in enumerate(dataset_budgets):
+ if int(budget) == target:
+ aw = dataset_aw_rel[bi]
+ me = dataset_max_err[bi]
+ ae = dataset_actual[bi]
+ if not np.isnan(aw):
+ print(f" teacher → elements={ae:6d} "
+ f"aw_rel={aw:.4f} max_err={me:.4f} (from dataset)")
+
+ return all_records
+
+
+# ============================================================================
+# Output: JSON, CSV, Pareto plots
+# ============================================================================
+
+
+def save_results(records: List[dict], out_dir: Path):
+ """Save eval_results.json and summary.csv."""
+ out_dir = Path(out_dir)
+ out_dir.mkdir(parents=True, exist_ok=True)
+
+ # JSON
+ json_path = out_dir / "eval_results.json"
+ with open(json_path, "w") as f:
+ json.dump(records, f, indent=2)
+ print(f" JSON saved: {json_path}")
+
+ # CSV
+ csv_path = out_dir / "summary.csv"
+ if records:
+ fieldnames = list(records[0].keys())
+ with open(csv_path, "w", newline="") as f:
+ writer = csv.DictWriter(f, fieldnames=fieldnames)
+ writer.writeheader()
+ writer.writerows(records)
+ print(f" CSV saved: {csv_path}")
+
+
+def plot_pareto(records: List[dict], out_dir: Path):
+ """Generate Pareto plots: aw_rel vs elements, max_err vs elements, aw_rel vs solves."""
+ import matplotlib
+ matplotlib.use("Agg")
+ import matplotlib.pyplot as plt
+
+ out_dir = Path(out_dir)
+ out_dir.mkdir(parents=True, exist_ok=True)
+
+ methods = sorted(set(r["method"] for r in records))
+ colors = {"gnn": "tab:blue", "geo": "tab:orange", "teacher": "tab:green"}
+
+ # --- aw_rel vs elements ---
+ fig, ax = plt.subplots(figsize=(7, 5))
+ for method in methods:
+ subset = [r for r in records if r["method"] == method]
+ elems = [r["actual_elements"] for r in subset]
+ aw = [r["aw_rel"] for r in subset]
+ ax.scatter(elems, aw, label=method, color=colors.get(method, "gray"), alpha=0.7, s=40)
+ ax.set_xlabel("Elements")
+ ax.set_ylabel("aw_rel")
+ ax.set_title("aw_rel vs Elements")
+ ax.legend()
+ ax.grid(True, alpha=0.3)
+ fig.tight_layout()
+ fig.savefig(out_dir / "aw_rel_vs_elements.png", dpi=100)
+ plt.close(fig)
+ print(f" Plot: {out_dir / 'aw_rel_vs_elements.png'}")
+
+ # --- max_err vs elements ---
+ fig, ax = plt.subplots(figsize=(7, 5))
+ for method in methods:
+ subset = [r for r in records if r["method"] == method]
+ elems = [r["actual_elements"] for r in subset]
+ me = [r["max_err"] for r in subset]
+ ax.scatter(elems, me, label=method, color=colors.get(method, "gray"), alpha=0.7, s=40)
+ ax.set_xlabel("Elements")
+ ax.set_ylabel("max_err")
+ ax.set_title("max_err vs Elements")
+ ax.legend()
+ ax.grid(True, alpha=0.3)
+ fig.tight_layout()
+ fig.savefig(out_dir / "max_err_vs_elements.png", dpi=100)
+ plt.close(fig)
+ print(f" Plot: {out_dir / 'max_err_vs_elements.png'}")
+
+ # --- aw_rel vs solves ---
+ fig, ax = plt.subplots(figsize=(7, 5))
+ for method in methods:
+ subset = [r for r in records if r["method"] == method]
+ solves = [r["num_solves"] for r in subset]
+ aw = [r["aw_rel"] for r in subset]
+ ax.scatter(solves, aw, label=method, color=colors.get(method, "gray"), alpha=0.7, s=40)
+ ax.set_xlabel("Num Solves")
+ ax.set_ylabel("aw_rel")
+ ax.set_title("aw_rel vs Solves")
+ ax.legend()
+ ax.grid(True, alpha=0.3)
+ fig.tight_layout()
+ fig.savefig(out_dir / "aw_rel_vs_solves.png", dpi=100)
+ plt.close(fig)
+ print(f" Plot: {out_dir / 'aw_rel_vs_solves.png'}")
+
+
+# ============================================================================
+# CLI
+# ============================================================================
+
+
+def main():
+ parser = argparse.ArgumentParser(description="Evaluate budget-conditioned models")
+ parser.add_argument("--checkpoint", type=str, required=True,
+ help="Path to budgeted GNN checkpoint")
+ parser.add_argument("--data-dir", type=str,
+ default=str(OUTLOOK_DIR / "data"),
+ help="Path to budget dataset directory")
+ parser.add_argument("--target-elements", type=str, required=True,
+ help="Comma-separated target element counts")
+ parser.add_argument("--models", type=str, default="gnn,geo",
+ help="Comma-separated models to evaluate (gnn,geo)")
+ parser.add_argument("--device", type=str, default="cpu")
+ parser.add_argument("--output-dir", type=str, default=str(RESULT_DIR))
+ parser.add_argument("--val-ratio", type=float, default=0.2)
+ parser.add_argument("--seed", type=int, default=42)
+ args = parser.parse_args()
+
+ device = args.device
+ if device == "cuda" and not torch.cuda.is_available():
+ print("CUDA unavailable, falling back to CPU")
+ device = "cpu"
+
+ target_elements_list = [int(x) for x in args.target_elements.split(",")]
+ models_to_eval = [x.strip() for x in args.models.split(",")]
+ out_dir = Path(args.output_dir)
+
+ print("=" * 60)
+ print("Budgeted Evaluation")
+ print("=" * 60)
+ print(f" Checkpoint: {args.checkpoint}")
+ print(f" Data dir: {args.data_dir}")
+ print(f" Target elements: {target_elements_list}")
+ print(f" Models: {models_to_eval}")
+ print(f" Device: {device}")
+ print(f" Output: {out_dir}")
+ print()
+
+ records = run_evaluation(
+ checkpoint_path=args.checkpoint,
+ data_dir=args.data_dir,
+ target_elements_list=target_elements_list,
+ models_to_eval=models_to_eval,
+ device=device,
+ val_ratio=args.val_ratio,
+ seed=args.seed,
+ )
+
+ print(f"\n{'='*60}")
+ print(f"Saving results to {out_dir}")
+ print(f"{'='*60}")
+ save_results(records, out_dir)
+ plot_pareto(records, out_dir)
+
+ # Print summary table
+ print(f"\n{'='*60}")
+ print("Summary")
+ print(f"{'='*60}")
+ print(f" {'method':8s} {'target':>7s} {'actual':>7s} {'overshoot':>10s} "
+ f"{'aw_rel':>8s} {'max_err':>8s} {'dofs':>6s}")
+ print(f" {'-'*8} {'-'*7} {'-'*7} {'-'*10} {'-'*8} {'-'*8} {'-'*6}")
+ for r in records:
+ print(f" {r['method']:8s} {r['target_elements']:7d} {r['actual_elements']:7d} "
+ f"{r['overshoot_ratio']:10.3f} {r['aw_rel']:8.4f} {r['max_err']:8.4f} "
+ f"{r['dofs']:6d}")
+
+ print("\nDone.")
+
+
+if __name__ == "__main__":
+ main()
diff --git a/outlook/src/eval_correction.py b/outlook/src/eval_correction.py
new file mode 100644
index 0000000..8701534
--- /dev/null
+++ b/outlook/src/eval_correction.py
@@ -0,0 +1,392 @@
+#!/usr/bin/env python3
+"""
+eval_correction.py
+==================
+Rollout evaluation of correction GNN on AMR refinement.
+
+From the initial mesh, drives iterative refinement using one of three scoring
+methods (physics-only, neural-only, hybrid). At every step the mesh geometry
+and physics features are recomputed, but there is **no** teacher_eta, **no**
+residual marking, and **no** intermediate FEM solve. Only the final mesh gets
+a single FEM solve for error evaluation.
+
+Methods
+-------
+physics — score = physics_score
+neural — score = model(features + physics_score)
+hybrid — score = alpha * norm(physics_score) + beta * norm(model_score)
+
+Usage
+-----
+python outlook/src/eval_correction.py \
+ --checkpoint outlook/ckpt/correction.pt \
+ --data-dir outlook/data_correction \
+ --target-elements 1000,2000,4000,8000 \
+ --mark-fraction 0.03 \
+ --max-steps 40 \
+ --methods physics,neural,hybrid \
+ --device cuda \
+ --output-dir outlook/result/correction/rollout
+"""
+
+import argparse
+import csv
+import json
+import sys
+from pathlib import Path
+
+import numpy as np
+
+_PROJECT_ROOT = Path(__file__).resolve().parent.parent.parent
+if str(_PROJECT_ROOT) not in sys.path:
+ sys.path.insert(0, str(_PROJECT_ROOT))
+
+import torch
+
+from outlook.src.rollout import run_rollout_to_budget, load_model
+
+
+# ============================================================================
+# Validation split (must mirror train_correction.py)
+# ============================================================================
+
+
+def get_validation_ids(n_samples: int, val_ratio: float, seed: int) -> set:
+ """Reproduce the train/val split from train_correction.py."""
+ rng = np.random.RandomState(seed)
+ indices = np.arange(n_samples)
+ rng.shuffle(indices)
+ n_val = max(1, int(n_samples * val_ratio))
+ return set(int(indices[i]) for i in range(n_val))
+
+
+# ============================================================================
+# Plotting helpers
+# ============================================================================
+
+
+def _plot_metric_vs_elements(ax, grouped, methods, metric, ylabel, title):
+ """Plot a metric vs actual_elements for each method on *ax*."""
+ COLORS = {"physics": "#2196F3", "neural": "#E91E63", "hybrid": "#4CAF50"}
+
+ for method in methods:
+ if method not in grouped:
+ continue
+ xs = sorted(grouped[method].keys())
+ means = [grouped[method][x][f"mean_{metric}"] for x in xs]
+ stds = [grouped[method][x][f"std_{metric}"] for x in xs]
+ ax.errorbar(xs, means, yerr=stds, label=method, color=COLORS.get(method),
+ marker="o", markersize=4, linewidth=1.5, capsize=3)
+
+ ax.set_xlabel("Actual elements")
+ ax.set_ylabel(ylabel)
+ ax.set_title(title)
+ ax.legend()
+ ax.grid(True, alpha=0.3)
+
+
+# ============================================================================
+# Main
+# ============================================================================
+
+
+def main():
+ parser = argparse.ArgumentParser(description="Rollout evaluation of correction GNN")
+ parser.add_argument("--checkpoint", type=str, required=True)
+ parser.add_argument("--data-dir", type=str, default="outlook/data_correction")
+ parser.add_argument("--target-elements", type=str, default="1000,2000,4000,8000")
+ parser.add_argument("--mark-fraction", type=float, default=0.03)
+ parser.add_argument("--max-steps", type=int, default=40)
+ parser.add_argument("--methods", type=str, default="physics,neural,hybrid")
+ parser.add_argument("--alpha", type=float, default=0.5)
+ parser.add_argument("--beta", type=float, default=0.5)
+ parser.add_argument("--budget-mode", type=str, default="fast",
+ choices=["fast", "strict"],
+ help="Budget enforcement: 'fast' (simple min-cap) or 'strict' (binary search + area safety)")
+ parser.add_argument("--device", type=str, default="cpu")
+ parser.add_argument("--output-dir", type=str, default="outlook/result/correction/rollout")
+ parser.add_argument("--seed", type=int, default=None,
+ help="Random seed (default: use training seed from checkpoint)")
+ args = parser.parse_args()
+
+ device = args.device
+ if device == "cuda" and not torch.cuda.is_available():
+ print("CUDA unavailable, falling back to CPU")
+ device = "cpu"
+
+ targets = [int(t) for t in args.target_elements.split(",")]
+ methods = [m.strip() for m in args.methods.split(",")]
+ output_dir = Path(args.output_dir)
+ output_dir.mkdir(parents=True, exist_ok=True)
+
+ # ── Load model (only if a neural method is requested) ─────────────────
+ need_model = any(m in ("neural", "hybrid") for m in methods)
+ model, normalizer, config = (None, None, None)
+ if need_model:
+ print(f"Loading checkpoint: {args.checkpoint}")
+ model, normalizer, config = load_model(args.checkpoint, device)
+ print(f" Model: latent_dim={config['latent_dim']}, "
+ f"mp_steps={config['num_mp_steps']}")
+
+ # ── Load sample params ────────────────────────────────────────────────
+ data_dir = Path(args.data_dir)
+ params_list_path = data_dir / "params_list.npz"
+ if not params_list_path.exists():
+ print(f"Error: {params_list_path} not found")
+ return
+
+ params_data = np.load(params_list_path)
+ params_array = params_data["params"]
+ n_samples = len(params_array)
+ print(f" Samples: {n_samples}")
+
+ # ── Determine validation split ────────────────────────────────────────
+ seed = args.seed if args.seed is not None else (config.get("seed", 42) if config else 42)
+ val_ratio = 0.2
+ val_ids = get_validation_ids(n_samples, val_ratio, seed)
+ sample_ids = sorted(val_ids)
+ print(f" Validation samples: {len(sample_ids)} (seed={seed}, val_ratio={val_ratio})")
+
+ # ── Run rollouts ──────────────────────────────────────────────────────
+ all_results = []
+
+ for sample_id in sample_ids:
+ row = params_array[sample_id]
+ params = {
+ "k": float(row[0]), "eps_r": float(row[1]),
+ "cx": float(row[2]), "cy": float(row[3]), "radius": float(row[4]),
+ }
+ print(f"\n[Sample {sample_id:04d}] k={params['k']:.2f} "
+ f"eps_r={params['eps_r']:.2f} r={params['radius']:.3f}")
+
+ for target in targets:
+ for method in methods:
+ result = run_rollout_to_budget(
+ method, params, target,
+ model=model, normalizer=normalizer,
+ mark_fraction=args.mark_fraction,
+ max_steps=args.max_steps,
+ device=device, seed=seed,
+ alpha=args.alpha, beta=args.beta,
+ budget_mode=args.budget_mode,
+ )
+ result.update({
+ "sample_id": sample_id, "method": method,
+ "target_elements": target, "params": params,
+ })
+ all_results.append(result)
+
+ aw_pct = f"{result['aw_rel']*100:.2f}%" if not np.isnan(result['aw_rel']) else "nan"
+ score_stats = result.get("score_stats", [])
+ if score_stats:
+ last = score_stats[-1]
+ print(f" {method:8s} target={target:6d} "
+ f"actual={result['actual_elements']:6d} "
+ f"steps={result['num_steps']:2d} aw_rel={aw_pct} "
+ f"score_mean={last['score_mean']:.3f} "
+ f"frac(>1)={last['fraction_gt1']:.3f} "
+ f"gap={last['gap']}")
+ else:
+ print(f" {method:8s} target={target:6d} "
+ f"actual={result['actual_elements']:6d} "
+ f"steps={result['num_steps']:2d} aw_rel={aw_pct}")
+
+ # ── Aggregate ─────────────────────────────────────────────────────────
+ from collections import defaultdict
+ stats = {} # (method, target) → aggregated stats
+ grouped = {} # method → {actual_elements → {mean_aw_rel, ...}}
+
+ for method in methods:
+ for target in targets:
+ rows = [r for r in all_results
+ if r["method"] == method and r["target_elements"] == target]
+ if not rows:
+ continue
+
+ aw_vals = [r["aw_rel"] for r in rows if not np.isnan(r["aw_rel"])]
+ me_vals = [r["max_err"] for r in rows if not np.isnan(r["max_err"])]
+ el_vals = [r["actual_elements"] for r in rows]
+ st_vals = [r["num_steps"] for r in rows]
+ sv_vals = [r["num_solves"] for r in rows]
+
+ stats[(method, target)] = {
+ "method": method, "target_elements": target,
+ "mean_actual_elements": float(np.mean(el_vals)),
+ "mean_aw_rel": float(np.mean(aw_vals)) if aw_vals else float("nan"),
+ "std_aw_rel": float(np.std(aw_vals)) if aw_vals else float("nan"),
+ "mean_max_err": float(np.mean(me_vals)) if me_vals else float("nan"),
+ "std_max_err": float(np.std(me_vals)) if me_vals else float("nan"),
+ "mean_num_steps": float(np.mean(st_vals)),
+ "mean_num_solves": float(np.mean(sv_vals)),
+ "n_samples": len(rows),
+ }
+
+ # Group by actual_elements for plotting (bin into 50-elem buckets)
+ method_rows = [r for r in all_results if r["method"] == method]
+ if not method_rows:
+ continue
+ bins = defaultdict(list)
+ for r in method_rows:
+ bucket = round(r["actual_elements"] / 50) * 50
+ bins[bucket].append(r)
+ grouped[method] = {}
+ for bucket in sorted(bins.keys()):
+ bucket_rows = bins[bucket]
+ aw = [r["aw_rel"] for r in bucket_rows if not np.isnan(r["aw_rel"])]
+ me = [r["max_err"] for r in bucket_rows if not np.isnan(r["max_err"])]
+ grouped[method][bucket] = {
+ "mean_aw_rel": float(np.mean(aw)) if aw else float("nan"),
+ "std_aw_rel": float(np.std(aw)) if aw else float("nan"),
+ "mean_max_err": float(np.mean(me)) if me else float("nan"),
+ "std_max_err": float(np.std(me)) if me else float("nan"),
+ "count": len(bucket_rows),
+ }
+
+ # ── Improvement ratios (per-sample, vs physics-only) ──────────────────
+ improvements = {}
+ for target in targets:
+ phys = {r["sample_id"]: r for r in all_results
+ if r["method"] == "physics" and r["target_elements"] == target}
+ for method in methods:
+ if method == "physics":
+ continue
+ others = {r["sample_id"]: r for r in all_results
+ if r["method"] == method and r["target_elements"] == target}
+ ratios_aw, ratios_me = [], []
+ for sid in phys:
+ if sid not in others:
+ continue
+ pa, oa = phys[sid]["aw_rel"], others[sid]["aw_rel"]
+ if not np.isnan(pa) and not np.isnan(oa) and pa > 1e-12:
+ ratios_aw.append((pa - oa) / pa * 100)
+ pm, om = phys[sid]["max_err"], others[sid]["max_err"]
+ if not np.isnan(pm) and not np.isnan(om) and pm > 1e-12:
+ ratios_me.append((pm - om) / pm * 100)
+ improvements[(method, target)] = {
+ "mean_aw_rel_improvement_pct": float(np.mean(ratios_aw)) if ratios_aw else 0.0,
+ "mean_max_err_improvement_pct": float(np.mean(ratios_me)) if ratios_me else 0.0,
+ "mean_actual_elements_physics": float(np.mean([phys[s]["actual_elements"] for s in phys])),
+ "mean_actual_elements_method": float(np.mean([others[s]["actual_elements"] for s in others])),
+ "n_paired": len(ratios_aw),
+ }
+
+ # ── Save JSON ─────────────────────────────────────────────────────────
+ # Strip non-serializable keys from per-sample results for JSON
+ _SKIP_KEYS = {"params", "mesh", "u_scat", "steps"}
+ json_results = []
+ for r in all_results:
+ entry = {k: v for k, v in r.items() if k not in _SKIP_KEYS}
+ # Convert numpy floats to Python floats
+ for k, v in entry.items():
+ if isinstance(v, (np.floating, np.integer)):
+ entry[k] = float(v)
+ # Convert numpy values inside score_stats
+ if "score_stats" in entry:
+ clean_stats = []
+ for s in entry["score_stats"]:
+ clean_stats.append({
+ sk: float(sv) if isinstance(sv, (np.floating, np.integer)) else sv
+ for sk, sv in s.items()
+ })
+ entry["score_stats"] = clean_stats
+ json_results.append(entry)
+
+ json_out = {
+ "results": json_results,
+ "summary": {f"{m}_{t}": s for (m, t), s in stats.items()},
+ "improvements": {f"{m}_{t}": imp for (m, t), imp in improvements.items()},
+ "config": {
+ "checkpoint": args.checkpoint,
+ "data_dir": args.data_dir,
+ "target_elements": targets,
+ "mark_fraction": args.mark_fraction,
+ "max_steps": args.max_steps,
+ "methods": methods,
+ "alpha": args.alpha,
+ "beta": args.beta,
+ "seed": seed,
+ "n_eval_samples": len(sample_ids),
+ },
+ }
+ json_path = output_dir / "eval_results.json"
+ with open(json_path, "w") as f:
+ json.dump(json_out, f, indent=2, default=str)
+ print(f"\nJSON → {json_path}")
+
+ # ── Save CSV ──────────────────────────────────────────────────────────
+ csv_path = output_dir / "summary.csv"
+ csv_cols = [
+ "method", "target_elements", "mean_actual_elements",
+ "mean_aw_rel", "std_aw_rel", "mean_max_err", "std_max_err",
+ "mean_num_steps", "mean_num_solves", "n_samples",
+ ]
+ with open(csv_path, "w", newline="") as f:
+ writer = csv.DictWriter(f, fieldnames=csv_cols)
+ writer.writeheader()
+ for (method, target) in sorted(stats.keys()):
+ writer.writerow({c: stats[(method, target)].get(c, "") for c in csv_cols})
+ print(f"CSV → {csv_path}")
+
+ # ── Plots ─────────────────────────────────────────────────────────────
+ import matplotlib
+ matplotlib.use("Agg")
+ import matplotlib.pyplot as plt
+
+ suptitle = (f"Rollout Evaluation | mark_fraction={args.mark_fraction} "
+ f"max_steps={args.max_steps}")
+
+ fig, ax = plt.subplots(figsize=(8, 5))
+ _plot_metric_vs_elements(ax, grouped, methods, "aw_rel",
+ "aw_rel", "Area-Weighted Relative Error")
+ fig.suptitle(suptitle, fontsize=12)
+ fig.tight_layout()
+ fig.savefig(output_dir / "aw_rel_vs_elements.png", dpi=150, bbox_inches="tight")
+ plt.close(fig)
+
+ fig, ax = plt.subplots(figsize=(8, 5))
+ _plot_metric_vs_elements(ax, grouped, methods, "max_err",
+ "max_err", "Max Pointwise Error")
+ fig.suptitle(suptitle, fontsize=12)
+ fig.tight_layout()
+ fig.savefig(output_dir / "max_err_vs_elements.png", dpi=150, bbox_inches="tight")
+ plt.close(fig)
+ print(f"Plots → {output_dir / 'aw_rel_vs_elements.png'}")
+ print(f" {output_dir / 'max_err_vs_elements.png'}")
+
+ # ── Print summary ─────────────────────────────────────────────────────
+ print(f"\n{'='*90}")
+ print(f"{'Method':8s} {'Target':>8s} {'Actual':>8s} {'aw_rel':>10s} "
+ f"{'max_err':>10s} {'Steps':>6s} {'Solves':>7s}")
+ print(f"{'-'*90}")
+ for (method, target) in sorted(stats.keys()):
+ s = stats[(method, target)]
+ aw_s = f"{s['mean_aw_rel']*100:.2f}%" if not np.isnan(s["mean_aw_rel"]) else "nan"
+ print(f"{s['method']:8s} {s['target_elements']:8d} "
+ f"{s['mean_actual_elements']:8.0f} {aw_s:>10s} "
+ f"{s['mean_max_err']:10.4f} {s['mean_num_steps']:6.1f} "
+ f"{s['mean_num_solves']:7.1f}")
+
+ print(f"\n{'='*90}")
+ print("Improvement vs physics-only (%)")
+ print(f"{'='*90}")
+ print(f"{'Method':8s} {'Target':>8s} {'aw_rel':>10s} {'max_err':>10s} "
+ f"{'Actual(method)':>15s} {'Actual(physics)':>16s} {'N':>4s}")
+ print(f"{'-'*90}")
+ for (method, target) in sorted(improvements.keys()):
+ imp = improvements[(method, target)]
+ print(f"{method:8s} {target:8d} "
+ f"{imp['mean_aw_rel_improvement_pct']:+9.1f}% "
+ f"{imp['mean_max_err_improvement_pct']:+9.1f}% "
+ f"{imp['mean_actual_elements_method']:15.0f} "
+ f"{imp['mean_actual_elements_physics']:16.0f} "
+ f"{imp['n_paired']:4d}")
+
+ print("\nDone.")
+
+
+# ============================================================================
+# Entry point
+# ============================================================================
+
+if __name__ == "__main__":
+ main()
diff --git a/outlook/src/feat.py b/outlook/src/feat.py
new file mode 100644
index 0000000..b9cfe48
--- /dev/null
+++ b/outlook/src/feat.py
@@ -0,0 +1,108 @@
+# 构建每个初始单元的 15 维特征 + budget_code（第 16 维）。
+"""feature_builder.py — Construct per-cell input features for the density network.
+
+Features are strictly limited to initial geometry and physical parameters.
+NO FEM solution, NO residual estimator, NO teacher information.
+"""
+
+import numpy as np
+
+from environment.fem_util import get_element_midpoints, get_triangle_areas_from_indices
+
+# Feature names for reference
+FEATURE_NAMES_V2 = [
+ "x", # 0 cell center x
+ "y", # 1 cell center y
+ "area", # 2 cell area
+ "dist_center", # 3 distance to cylinder center
+ "signed_dist", # 4 signed distance to interface
+ "inside", # 5 inside dielectric (0/1)
+ "k", # 6 wave number
+ "eps_r", # 7 relative permittivity
+ "radius", # 8 cylinder radius
+ "cx", # 9 cylinder center x
+ "cy", # 10 cylinder center y
+ "k_h", # 11 k * sqrt(area)
+ "k_eps_h", # 12 k * sqrt(eps_r_local) * sqrt(area)
+ "sin_kx", # 13 sin(k*x) incident phase
+ "cos_kx", # 14 cos(k*x) incident phase
+ "budget_ratio", # 15 budget ratio conditioning
+]
+
+
+def build_initial_cell_features(initial_mesh, params, budget_ratio=1.0):
+ """Construct 16-dim per-cell features for the density prediction network.
+
+ Parameters
+ ----------
+ initial_mesh : skfem.Mesh
+ params : dict
+ Must contain: k, eps_r, cx, cy, radius
+ budget_ratio : float
+ Target budget as fraction of teacher mesh size (default 1.0).
+
+ Returns
+ -------
+ features : (N_cells, 16) float32
+ """
+ k = params["k"]
+ eps_r_val = params["eps_r"]
+ cx = params["cx"]
+ cy = params["cy"]
+ radius = params["radius"]
+
+ midpoints = get_element_midpoints(initial_mesh)
+ x, y = midpoints[:, 0], midpoints[:, 1]
+
+ areas = get_triangle_areas_from_indices(
+ positions=initial_mesh.p.T, triangle_indices=initial_mesh.t.T
+ )
+
+ dist_to_center = np.sqrt((x - cx) ** 2 + (y - cy) ** 2)
+ signed_dist = dist_to_center - radius
+ inside = ((x - cx) ** 2 + (y - cy) ** 2 <= radius ** 2).astype(np.float32)
+ eps_r_local = np.where(inside > 0.5, eps_r_val, 1.0)
+
+ sqrt_area = np.sqrt(np.maximum(areas, 1e-15))
+ k_h = k * sqrt_area
+ k_eps_h = k * np.sqrt(eps_r_local) * sqrt_area
+ sin_kx = np.sin(k * x)
+ cos_kx = np.cos(k * x)
+
+ features = np.column_stack([
+ x, y, areas, dist_to_center, signed_dist, inside,
+ np.full_like(x, k), np.full_like(x, eps_r_val),
+ np.full_like(x, radius), np.full_like(x, cx), np.full_like(x, cy),
+ k_h, k_eps_h, sin_kx, cos_kx,
+ np.full_like(x, budget_ratio),
+ ]).astype(np.float32)
+
+ return features
+
+
+def append_budget_feature(
+ features_base: np.ndarray,
+ target_elements: float,
+ n_init: int,
+) -> np.ndarray:
+ """Append budget_code as the 16th feature dimension.
+
+ budget_code = log(target_elements / n_init)
+
+ Parameters
+ ----------
+ features_base : (n_init, 15) float32
+ Base 15-dim features (no budget info).
+ target_elements : int or float
+ Target element budget.
+ n_init : int
+ Number of initial mesh cells.
+
+ Returns
+ -------
+ features : (n_init, 16) float32
+ Features with budget_code appended as last column.
+ """
+ budget_code = np.log(target_elements / n_init)
+ budget_col = np.full((n_init, 1), budget_code, dtype=np.float32)
+ return np.concatenate([features_base, budget_col], axis=1)
diff --git a/outlook/src/gen.py b/outlook/src/gen.py
new file mode 100644
index 0000000..ac56a55
--- /dev/null
+++ b/outlook/src/gen.py
@@ -0,0 +1,712 @@
+#!/usr/bin/env python3
+"""
+gen.py — Step-wise physics-guided refinement correction data generation.
+
+For each PDE sample, runs a residual-driven AMR loop and at every step saves:
+ - cell features (15-dim)
+ - physics_score (h / lambda_eff per cell)
+ - teacher_eta (residual estimator)
+ - teacher_mark (top-fraction by eta)
+ - physics_mark (top-fraction by physics_score)
+ - correction_label = teacher_mark - physics_mark
+
+Output: one .npz per (sample, step), plus a summary.json.
+
+Usage:
+ python outlook/src/gen.py --n-samples 20 --max-elements 12000 --max-steps 20
+"""
+
+import argparse
+import json
+import sys
+import time
+from pathlib import Path
+
+import numpy as np
+
+_PROJECT_ROOT = Path(__file__).resolve().parent.parent.parent
+sys.path.insert(0, str(_PROJECT_ROOT))
+
+from environment.helmholtz import (
+ HelmholtzProblem,
+ _compute_eps_r_at_midpoints,
+ _compute_residual_indicator,
+)
+
+OUTLOOK_DIR = _PROJECT_ROOT / "outlook"
+DEFAULT_DATA_DIR = OUTLOOK_DIR / "data"
+
+
+# ============================================================================
+# Parameter sampling
+# ============================================================================
+
+
+def sample_parameters(n_samples: int, rng: np.random.RandomState) -> list:
+ """Sample Helmholtz scattering parameters uniformly.
+
+ Ranges: k∈[3,15], eps_r∈[2,8], cx/cy∈[0.2,0.8], radius∈[0.05,0.25].
+ """
+ params_list = []
+ for _ in range(n_samples):
+ params_list.append({
+ "k": float(rng.uniform(3.0, 15.0)),
+ "eps_r": float(rng.uniform(2.0, 8.0)),
+ "cx": float(rng.uniform(0.2, 0.8)),
+ "cy": float(rng.uniform(0.2, 0.8)),
+ "radius": float(rng.uniform(0.05, 0.25)),
+ })
+ return params_list
+
+
+# ============================================================================
+# FEM config
+# ============================================================================
+
+
+
+# ============================================================================
+# Mesh quality diagnostics
+# ============================================================================
+
+
+def _compute_triangle_angles(p, t):
+ """Compute min/max angles (degrees) for all triangles.
+
+ Parameters
+ ----------
+ p : (2, n_vertices)
+ t : (3, n_elements)
+
+ Returns
+ -------
+ min_angle, max_angle : (n_elements,) arrays in degrees
+ """
+ v0 = p[:, t[0]] # (2, n_elem)
+ v1 = p[:, t[1]]
+ v2 = p[:, t[2]]
+
+ e0 = v2 - v1 # edge opposite vertex 0
+ e1 = v0 - v2 # edge opposite vertex 1
+ e2 = v1 - v0 # edge opposite vertex 2
+
+ def _angle(a, b):
+ """Angle between vectors a and b (each (2, n))."""
+ cos = (a[0] * b[0] + a[1] * b[1]) / (
+ np.sqrt(a[0]**2 + a[1]**2) * np.sqrt(b[0]**2 + b[1]**2) + 1e-30
+ )
+ return np.degrees(np.arccos(np.clip(cos, -1, 1)))
+
+ # Angle at vertex 0: between edges e1 (toward v0 from v2) and -e2 (toward v0 from v1)
+ # Actually: at vertex 0, the two edges are (v1 - v0) and (v2 - v0) = -e2 and e1
+ a0 = _angle(-e2, e1) # angle at v0
+ a1 = _angle(-e0, e2) # angle at v1
+ a2 = _angle(-e1, e0) # angle at v2
+
+ all_angles = np.stack([a0, a1, a2], axis=0) # (3, n_elem)
+ return all_angles.min(axis=0), all_angles.max(axis=0)
+
+
+def _compute_aspect_ratio(p, t):
+ """Compute aspect ratio = circumradius / (2 * inradius) for each triangle.
+
+ Equivalent to max_edge / (2 * sqrt(3) * inradius) for equilateral.
+ Uses formula: aspect = (a*b*c) / (4*area * (a+b+c)/2) / (2*r_in)
+ Simplified: aspect = (a*b*c) / (8 * area * r_in) where r_in = 2*area/perimeter.
+ """
+ v0 = p[:, t[0]]
+ v1 = p[:, t[1]]
+ v2 = p[:, t[2]]
+
+ # Edge lengths
+ e01 = np.sqrt((v1[0] - v0[0])**2 + (v1[1] - v0[1])**2)
+ e12 = np.sqrt((v2[0] - v1[0])**2 + (v2[1] - v1[1])**2)
+ e20 = np.sqrt((v0[0] - v2[0])**2 + (v0[1] - v2[1])**2)
+
+ # Area via cross product
+ area = 0.5 * np.abs(
+ (v1[0] - v0[0]) * (v2[1] - v0[1]) - (v2[0] - v0[0]) * (v1[1] - v0[1])
+ )
+
+ # Inradius
+ perimeter = e01 + e12 + e20
+ r_in = 2.0 * area / (perimeter + 1e-30)
+
+ # Circumradius
+ r_circ = (e01 * e12 * e20) / (4.0 * area + 1e-30)
+
+ return r_circ / (r_in + 1e-30)
+
+
+def _mesh_quality_report(mesh, label="mesh"):
+ """Print and return mesh quality metrics.
+
+ Returns dict with keys: n_elem, min_area, min_angle, max_aspect_ratio.
+ Raises RuntimeError if degenerate elements are found.
+ """
+ p = mesh.p
+ t = mesh.t
+
+ # Areas
+ v0 = p[:, t[0]]
+ v1 = p[:, t[1]]
+ v2 = p[:, t[2]]
+ areas = 0.5 * np.abs(
+ (v1[0] - v0[0]) * (v2[1] - v0[1]) - (v2[0] - v0[0]) * (v1[1] - v0[1])
+ )
+
+ # Degenerate check
+ bad = np.where(~np.isfinite(areas) | (areas <= 1e-14))[0]
+ if len(bad) > 0:
+ raise RuntimeError(
+ f"[{label}] {len(bad)} degenerate elements (min_area={areas.min():.3e})"
+ )
+
+ # Angles
+ min_angle, max_angle = _compute_triangle_angles(p, t)
+
+ # Aspect ratio
+ aspect = _compute_aspect_ratio(p, t)
+
+ report = {
+ "n_elem": t.shape[1],
+ "min_area": float(areas.min()),
+ "min_angle": float(min_angle.min()),
+ "max_angle": float(max_angle.max()),
+ "max_aspect_ratio": float(aspect.max()),
+ "mean_aspect_ratio": float(aspect.mean()),
+ }
+
+ if label is not None:
+ print(
+ f" [{label}] elems={report['n_elem']:5d} "
+ f"min_area={report['min_area']:.3e} "
+ f"min_angle={report['min_angle']:.1f}° "
+ f"max_aspect={report['max_aspect_ratio']:.2f}"
+ )
+
+ return report
+
+
+# ============================================================================
+# Initial mesh: uniform base + isotropic local refinement
+# ============================================================================
+
+
+def build_physics_safe_initial_mesh(
+ params: dict,
+ q: float = 2.0,
+ max_initial_elements: int = 5000,
+ max_pre_refine_rounds: int = 15,
+ verbose: bool = False,
+):
+ """Create a physics-adapted initial mesh via uniform base + local refinement.
+
+ Uses score = max_edge / h_target as the refinement criterion.
+ Refines all cells with score > 1 (under-resolved) until one of:
+ - No cells have score > 1 (all physics-safe)
+ - max_initial_elements reached
+ - max_pre_refine_rounds exhausted
+
+ This is the *initial mesh generation* phase — distinct from the
+ rollout-to-budget phase which continues refining top-k cells
+ regardless of score values.
+
+ Parameters
+ ----------
+ params : dict with keys k, eps_r, cx, cy, radius
+ q : float
+ Elements per wavelength (default 2).
+ max_initial_elements : int
+ Hard cap on element count during pre-refinement.
+ max_pre_refine_rounds : int
+ Maximum number of pre-refinement iterations.
+ verbose : bool
+ Print quality report after each round.
+
+ Returns
+ -------
+ mesh : MeshTri
+ """
+ from skfem import MeshTri
+
+ k = params["k"]
+ eps_r = params["eps_r"]
+ cx, cy, radius = params["cx"], params["cy"], params["radius"]
+
+ lambda0 = 2.0 * np.pi / k
+ lambda_eff = 2.0 * np.pi / (k * np.sqrt(eps_r))
+
+ h_out = lambda0 / q # target cell size outside scatterer
+ h_in = lambda_eff / q # target cell size inside scatterer
+
+ # ── Step 1: uniform base mesh ──
+ # Choose n so that uniform cell size ≤ min(h_out, h_in)
+ h_min = min(h_out, h_in)
+ n_side = max(16, int(np.ceil(1.0 / h_min)))
+ # Cap at a reasonable starting density
+ n_side = min(n_side, 64)
+
+ mesh = MeshTri.init_tensor(
+ np.linspace(0, 1, n_side + 1),
+ np.linspace(0, 1, n_side + 1),
+ )
+
+ # ── Step 2: iterative local refinement ──
+ # Two-density mesh: h_in inside scatterer, h_out outside. No extra interface band.
+
+ for rnd in range(max_pre_refine_rounds):
+ n_elem = mesh.t.shape[1]
+ if n_elem >= max_initial_elements:
+ break
+
+ p = mesh.p
+ t = mesh.t
+
+ # Per-cell geometry
+ v0 = p[:, t[0]]
+ v1 = p[:, t[1]]
+ v2 = p[:, t[2]]
+
+ # Midpoints
+ mx = (v0[0] + v1[0] + v2[0]) / 3.0
+ my = (v0[1] + v1[1] + v2[1]) / 3.0
+
+ # Max edge length per cell
+ e0 = np.sqrt((v1[0] - v0[0])**2 + (v1[1] - v0[1])**2)
+ e1 = np.sqrt((v2[0] - v1[0])**2 + (v2[1] - v1[1])**2)
+ e2 = np.sqrt((v0[0] - v2[0])**2 + (v0[1] - v2[1])**2)
+ max_edge = np.maximum(np.maximum(e0, e1), e2)
+
+ # Signed distance to scatterer boundary
+ dist = np.sqrt((mx - cx)**2 + (my - cy)**2)
+ inside = dist <= radius
+
+ # Local h_target: two densities only
+ h_target = np.where(inside, h_in, h_out)
+
+ # Mark cells where max_edge exceeds h_target
+ marked = np.where(max_edge > h_target)[0]
+
+ if len(marked) == 0:
+ break
+
+ # Don't overshoot: binary-search for largest batch that stays within budget.
+ # mesh.refined() cascades to neighbors for conformity, so the actual
+ # element count can be 3-6× the marked count — a fixed divisor is unreliable.
+ remaining = max_initial_elements - n_elem
+ if remaining <= 0:
+ break
+
+ # Sort by severity (worst first) with physical tie-breakers
+ ratio = max_edge / (h_target + 1e-30)
+ # Tie-breaker for identical ratio: interface proximity → inside preference
+ signed_dist = dist - radius
+ abs_sd = np.abs(signed_dist[marked])
+ inside_flag = inside[marked].astype(np.float32)
+ tie_key = -abs_sd + inside_flag # higher = closer to interface & inside
+ # Composite: ratio dominates (×1e6), tie_key breaks ties
+ composite = ratio[marked] * 1e6 + tie_key
+ order = np.argsort(composite)[::-1] # descending
+ marked_sorted = marked[order]
+
+ lo, hi = 1, len(marked_sorted)
+ best_n = 0
+ best_mesh = mesh
+ while lo <= hi:
+ mid = (lo + hi) // 2
+ trial = mesh.refined(marked_sorted[:mid])
+ if trial.t.shape[1] <= max_initial_elements:
+ best_n = mid
+ best_mesh = trial
+ lo = mid + 1
+ else:
+ hi = mid - 1
+
+ if best_n == 0:
+ # Even one cell overshoots — skip refinement to stay within budget
+ break
+
+ mesh = best_mesh
+
+ # ── Final validation + one-line summary ──
+ report = _mesh_quality_report(mesh, "initial mesh" if verbose else None)
+
+ if report["min_angle"] < 10.0:
+ import warnings
+ warnings.warn(
+ f"Initial mesh has poor quality: min_angle={report['min_angle']:.1f}°",
+ stacklevel=2,
+ )
+
+ return mesh
+
+
+# Backward-compatible alias
+make_initial_mesh = build_physics_safe_initial_mesh
+
+
+def make_fem_config(params: dict) -> dict:
+ return {
+ "helmholtz": {
+ "wave_number": params["k"],
+ "wave_number_mode": "fixed",
+ "scatterer": {
+ "mode": "fixed",
+ "cx": params["cx"],
+ "cy": params["cy"],
+ "radius": params["radius"],
+ "eps_r": params["eps_r"],
+ },
+ "k_ref": 6.0,
+ "k_exponent": 2.0,
+ },
+ "domain": {
+ "boundary": [0, 0, 1, 1],
+ "initial_num_elements": 50,
+ },
+ }
+
+
+
+# ============================================================================
+# Physics score: h / lambda_eff
+# ============================================================================
+
+
+def compute_physics_score(mesh, params: dict, q: float = 2.0) -> np.ndarray:
+ """Compute per-cell physics score = max_edge / h_target.
+
+ h_target = lambda_eff / q, where lambda_eff depends on eps_r_local.
+ A score > 1 means the cell is under-resolved and needs refinement.
+ The score correctly reflects epsilon contrast: inside the scatterer
+ h_target is sqrt(eps_r) times smaller, so the same cell is more
+ "under-resolved" inside than outside.
+
+ Parameters
+ ----------
+ mesh : skfem.Mesh
+ params : dict with keys k, eps_r, cx, cy, radius
+ q : float
+ Target elements per wavelength (default 2).
+ """
+ k = params["k"]
+ eps_r_val = params["eps_r"]
+ cx = params["cx"]
+ cy = params["cy"]
+ radius = params["radius"]
+
+ p = mesh.p
+ t = mesh.t
+ v0, v1, v2 = p[:, t[0]], p[:, t[1]], p[:, t[2]]
+
+ # Max edge length per cell
+ e0 = np.sqrt((v1[0] - v0[0])**2 + (v1[1] - v0[1])**2)
+ e1 = np.sqrt((v2[0] - v1[0])**2 + (v2[1] - v1[1])**2)
+ e2 = np.sqrt((v0[0] - v2[0])**2 + (v0[1] - v2[1])**2)
+ max_edge = np.maximum(np.maximum(e0, e1), e2)
+
+ # Midpoints
+ mx = (v0[0] + v1[0] + v2[0]) / 3.0
+ my = (v0[1] + v1[1] + v2[1]) / 3.0
+
+ # Local wavelength: lambda_eff depends on whether cell is inside scatterer
+ inside = ((mx - cx)**2 + (my - cy)**2 <= radius**2)
+ lambda_eff = np.where(
+ inside,
+ 2.0 * np.pi / (k * np.sqrt(eps_r_val)),
+ 2.0 * np.pi / k,
+ )
+
+ h_target = lambda_eff / q
+
+ return (max_edge / h_target).astype(np.float32)
+
+
+
+# ============================================================================
+# Top-fraction marking
+# ============================================================================
+
+
+def compute_top_fraction_mark(scores: np.ndarray, fraction: float,
+ signed_dist=None, is_inside=None,
+ domain_center=None) -> np.ndarray:
+ """Return binary (0/1) array marking the top `fraction` of cells by score.
+
+ Uses deterministic top-k selection with physical tie-breaking when
+ many cells share the same score (e.g. on a uniform mesh where
+ physics_score has only 2 unique values).
+ """
+ n = len(scores)
+ n_mark = max(1, int(n * fraction))
+ if n_mark >= n:
+ return np.ones(n, dtype=np.int32)
+ marks = np.zeros(n, dtype=np.int32)
+ if signed_dist is not None and is_inside is not None and domain_center is not None:
+ from outlook.src.rollout import _topk_indices
+ idx, _ = _topk_indices(scores, n_mark, signed_dist, is_inside, domain_center)
+ marks[idx] = 1
+ else:
+ marks[np.argsort(scores)[-n_mark:]] = 1
+ return marks
+
+
+# ============================================================================
+# Main: step-wise correction dataset generation
+# ============================================================================
+
+
+def generate_correction_dataset(
+ n_samples: int = 100,
+ max_elements: int = 20000,
+ max_steps: int = 20,
+ mark_fraction: float = 0.03,
+ seed: int = 42,
+ out_dir=None,
+):
+ """Generate step-wise correction dataset.
+
+ For each sample:
+ 1. Create problem, get initial mesh
+ 2. AMR loop: solve → eta → physics_score → marks → save step .npz → refine
+ 3. Stop when elements >= max_elements or max_steps reached
+ """
+ if out_dir is None:
+ out_dir = DEFAULT_DATA_DIR
+ out_dir = Path(out_dir)
+ out_dir.mkdir(parents=True, exist_ok=True)
+
+ rng = np.random.RandomState(seed)
+ params_list = sample_parameters(n_samples, rng)
+
+ # Save parameter index
+ params_array = np.array(
+ [[p["k"], p["eps_r"], p["cx"], p["cy"], p["radius"]] for p in params_list],
+ dtype=np.float32,
+ )
+ np.savez(out_dir / "params_list.npz", params=params_array)
+
+ # Accumulate per-step stats for summary
+ all_step_stats = []
+ total_files = 0
+
+ for idx, params in enumerate(params_list):
+ t_start = time.perf_counter()
+
+ try:
+ # ---- 1. Create problem ----
+ fem_config = make_fem_config(params)
+ problem = HelmholtzProblem(
+ fem_config=fem_config,
+ random_state=np.random.RandomState(rng.randint(0, 2**31)),
+ )
+ mesh = build_physics_safe_initial_mesh(params)
+ n_steps_done = 0
+
+ print(f"\n [{idx:04d}/{n_samples}] "
+ f"k={params['k']:.2f} eps_r={params['eps_r']:.2f} "
+ f"cx={params['cx']:.2f} cy={params['cy']:.2f} "
+ f"radius={params['radius']:.3f}")
+
+ from skfem import Basis, ElementTriP1
+
+ for step in range(max_steps):
+ n_elem = mesh.t.shape[1]
+ if n_elem >= max_elements:
+ break
+
+ # ---- 2. FEM solve ----
+ basis = Basis(mesh, ElementTriP1())
+ u_scat = problem.calculate_solution(basis=basis, cache=False)
+
+ # ---- 3. Residual indicator (teacher signal) ----
+ eps_r_arr = _compute_eps_r_at_midpoints(
+ mesh,
+ cx=problem._cx, cy=problem._cy,
+ radius=problem._radius, eps_r_in=problem._eps_r,
+ )
+ eta = _compute_residual_indicator(
+ mesh, u_scat, k=problem._k, eps_r=eps_r_arr
+ )
+
+ # ---- 4. Physics score ----
+ physics_score = compute_physics_score(mesh, params)
+
+ # ---- 5. Mie error (before refinement) ----
+ aw_rel = np.nan
+ max_err = np.nan
+ try:
+ from outlook.src.metrics import compute_mie_error
+ err = compute_mie_error(mesh, u_scat, params)
+ aw_rel = err["aw_rel"]
+ max_err = err["max_err"]
+ except Exception:
+ pass
+
+ # ---- 6. Marks (with physical tie-breaking) ----
+ _p = mesh.p
+ _t = mesh.t
+ _mx = (_p[0, _t[0]] + _p[0, _t[1]] + _p[0, _t[2]]) / 3.0
+ _my = (_p[1, _t[0]] + _p[1, _t[1]] + _p[1, _t[2]]) / 3.0
+ _cx, _cy, _r = params["cx"], params["cy"], params["radius"]
+ _dist = np.sqrt((_mx - _cx)**2 + (_my - _cy)**2)
+ _sd = _dist - _r
+ _inside = _dist <= _r
+ _dc = np.array([(_p[0].min() + _p[0].max()) / 2.0,
+ (_p[1].min() + _p[1].max()) / 2.0])
+ teacher_mark = compute_top_fraction_mark(
+ eta, mark_fraction, _sd, _inside, _dc)
+ physics_mark = compute_top_fraction_mark(
+ physics_score, mark_fraction, _sd, _inside, _dc)
+ correction_label = teacher_mark - physics_mark # -1, 0, or +1
+
+ # ---- 7. Features & edge_index ----
+ from outlook.src.feat import build_initial_cell_features
+ from outlook.src.graph import build_edge_index_np
+ features = build_initial_cell_features(mesh, params)[:, :15]
+ edge_index = build_edge_index_np(mesh)
+
+ # ---- 8. Save step .npz ----
+ fname = f"sample{idx:04d}_step{step:03d}.npz"
+ np.savez_compressed(
+ out_dir / fname,
+ features=features, # (n_elem, 15) float32
+ edge_index=edge_index, # (2, n_edges) int64
+ physics_score=physics_score, # (n_elem,) float32
+ teacher_eta=eta.astype(np.float64), # (n_elem,) float64
+ teacher_mark=teacher_mark, # (n_elem,) int32
+ physics_mark=physics_mark, # (n_elem,) int32
+ correction_label=correction_label, # (n_elem,) int32
+ elements=np.int64(n_elem),
+ step=np.int64(step),
+ aw_rel_before=np.float64(aw_rel),
+ max_err_before=np.float64(max_err),
+ k=np.float64(params["k"]),
+ eps_r=np.float64(params["eps_r"]),
+ cx=np.float64(params["cx"]),
+ cy=np.float64(params["cy"]),
+ radius=np.float64(params["radius"]),
+ )
+ total_files += 1
+
+ # Step stats
+ overlap = int(np.sum((teacher_mark == 1) & (physics_mark == 1)))
+ n_teacher = int(np.sum(teacher_mark))
+ n_physics = int(np.sum(physics_mark))
+ n_pos = int(np.sum(correction_label == 1))
+ n_neg = int(np.sum(correction_label == -1))
+
+ all_step_stats.append({
+ "sample": idx,
+ "step": step,
+ "elements": n_elem,
+ "n_teacher": n_teacher,
+ "n_physics": n_physics,
+ "overlap": overlap,
+ "n_pos": n_pos,
+ "n_neg": n_neg,
+ })
+
+ aw_str = f"{aw_rel:.4f}" if not np.isnan(aw_rel) else "N/A"
+ print(f" step {step:2d}: elem={n_elem:6d} "
+ f"teacher_mark={n_teacher:4d} physics_mark={n_physics:4d} "
+ f"overlap={overlap:4d} correction +{n_pos}/-{n_neg} "
+ f"aw_rel={aw_str}")
+
+ # ---- 9. Refine by eta (shared helper) ----
+ from outlook.src.rollout import _refine_by_eta
+ refined = _refine_by_eta(mesh, eta, mark_fraction, max_elements)
+ if refined is None:
+ break
+ mesh = refined
+ n_steps_done += 1
+
+ elapsed = time.perf_counter() - t_start
+ print(f" Done: {n_steps_done} steps, {elapsed:.1f}s")
+
+ except Exception as e:
+ print(f" [{idx:04d}/{n_samples}] FAILED: {type(e).__name__}: {e}")
+ import traceback
+ traceback.print_exc()
+ continue
+
+ # ---- Summary ----
+ print(f"\n{'='*60}")
+ print(f"Done: {total_files} step files saved to {out_dir}")
+
+ if not all_step_stats:
+ return
+
+ elems = [s["elements"] for s in all_step_stats]
+ t_marks = [s["n_teacher"] for s in all_step_stats]
+ p_marks = [s["n_physics"] for s in all_step_stats]
+ overlaps = [s["overlap"] for s in all_step_stats]
+ n_pos = [s["n_pos"] for s in all_step_stats]
+ n_neg = [s["n_neg"] for s in all_step_stats]
+
+ total_cells = sum(elems)
+ summary = {
+ "total_steps": len(all_step_stats),
+ "total_files": total_files,
+ "mean_elements": float(np.mean(elems)),
+ "mean_teacher_mark_ratio": float(np.mean([t / max(e, 1) for t, e in zip(t_marks, elems)])),
+ "mean_physics_mark_ratio": float(np.mean([p / max(e, 1) for p, e in zip(p_marks, elems)])),
+ "mean_overlap_teacher_physics": float(np.mean(overlaps)),
+ "mean_correction_pos_ratio": float(np.mean([p / max(e, 1) for p, e in zip(n_pos, elems)])),
+ "mean_correction_neg_ratio": float(np.mean([n / max(e, 1) for n, e in zip(n_neg, elems)])),
+ }
+
+ summary_path = out_dir / "summary.json"
+ with open(summary_path, "w") as f:
+ json.dump(summary, f, indent=2)
+
+ print(f"\n Summary:")
+ for k, v in summary.items():
+ print(f" {k}: {v}")
+ print(f"\n Saved: {summary_path}")
+
+
+# ============================================================================
+# CLI
+# ============================================================================
+
+
+def main():
+ parser = argparse.ArgumentParser(
+ description="Generate step-wise physics-guided refinement correction dataset"
+ )
+ parser.add_argument("--n-samples", type=int, default=100)
+ parser.add_argument("--max-elements", type=int, default=20000)
+ parser.add_argument("--max-steps", type=int, default=20)
+ parser.add_argument("--mark-fraction", type=float, default=0.03,
+ help="Top fraction for both teacher and physics marks (default: 0.03)")
+ parser.add_argument("--seed", type=int, default=42)
+ parser.add_argument("--output-dir", type=str, default=None)
+ args = parser.parse_args()
+
+ out_dir = Path(args.output_dir) if args.output_dir else DEFAULT_DATA_DIR
+
+ print("=" * 60)
+ print("Step-Wise Correction Dataset Generation")
+ print("=" * 60)
+ print(f" Samples: {args.n_samples}")
+ print(f" Max elements: {args.max_elements}")
+ print(f" Max steps: {args.max_steps}")
+ print(f" Mark fraction: {args.mark_fraction}")
+ print(f" Seed: {args.seed}")
+ print(f" Output: {out_dir}")
+ print()
+
+ generate_correction_dataset(
+ n_samples=args.n_samples,
+ max_elements=args.max_elements,
+ max_steps=args.max_steps,
+ mark_fraction=args.mark_fraction,
+ seed=args.seed,
+ out_dir=out_dir,
+ )
+
+
+if __name__ == "__main__":
+ main()
diff --git a/outlook/src/gnn.py b/outlook/src/gnn.py
new file mode 100644
index 0000000..d29fa0a
--- /dev/null
+++ b/outlook/src/gnn.py
@@ -0,0 +1,244 @@
+# DensityGNN 模型：消息传递 + 全局虚拟节点 + 密度预测头。
+"""density_gnn.py — Supervised GNN for final mesh density prediction.
+
+Reuses the message passing architecture from src/network.py (EdgeModule,
+NodeModule, GlobalVirtualNode) but replaces Actor-Critic heads with a
+simple per-node density regression head.
+
+Input: initial mesh graph (node features, edge_index, edge_attr)
+Output: per-cell density score (continuous, trained on log_rho)
+"""
+
+import copy
+
+import torch
+import torch.nn as nn
+from torch_geometric.data import Data
+from torch_geometric.utils import dropout_edge
+from torch_scatter import scatter_add, scatter_mean
+
+
+# ── Activation helper ──
+
+def _get_activation(name: str) -> nn.Module:
+ name = name.lower()
+ if name == "relu":
+ return nn.ReLU()
+ elif name == "leakyrelu":
+ return nn.LeakyReLU()
+ elif name == "elu":
+ return nn.ELU()
+ elif name in ("swish", "silu"):
+ return nn.SiLU()
+ elif name == "gelu":
+ return nn.GELU()
+ elif name == "tanh":
+ return nn.Tanh()
+ raise ValueError(f"Unknown activation '{name}'")
+
+
+# ── Latent MLP (latent_dim → latent_dim) ──
+
+class LatentMLP(nn.Module):
+ """MLP that operates in latent space (dim in == dim out == latent_dim)."""
+
+ def __init__(self, in_features: int, latent_dim: int, num_layers: int = 2,
+ activation: str = "leakyrelu"):
+ super().__init__()
+ layers = []
+ prev = in_features
+ for _ in range(num_layers):
+ layers.append(nn.Linear(prev, latent_dim))
+ layers.append(_get_activation(activation))
+ prev = latent_dim
+ self.mlp = nn.Sequential(*layers)
+
+ def forward(self, x: torch.Tensor) -> torch.Tensor:
+ return self.mlp(x)
+
+
+# ── Edge update: MLP([src_node | dst_node | edge_attr]) ──
+
+class EdgeModule(nn.Module):
+ def __init__(self, latent_dim: int, num_layers: int = 2,
+ activation: str = "leakyrelu"):
+ super().__init__()
+ self.mlp = LatentMLP(3 * latent_dim, latent_dim, num_layers, activation)
+
+ def forward(self, graph: Data):
+ src, dst = graph.edge_index
+ agg = torch.cat([graph.x[src], graph.x[dst], graph.edge_attr], dim=-1)
+ graph.edge_attr = self.mlp(agg)
+
+
+# ── Node update: MLP([node | scatter_mean(incoming_edges)]) ──
+
+class NodeModule(nn.Module):
+ def __init__(self, latent_dim: int, num_layers: int = 2,
+ activation: str = "leakyrelu"):
+ super().__init__()
+ self.mlp = LatentMLP(2 * latent_dim, latent_dim, num_layers, activation)
+
+ def forward(self, graph: Data):
+ _, dst = graph.edge_index
+ agg_edges = scatter_mean(graph.edge_attr, dst, dim=0,
+ dim_size=graph.x.shape[0])
+ agg = torch.cat([graph.x, agg_edges], dim=-1)
+ graph.x = self.mlp(agg)
+
+
+# ── Single message passing step with residual + LayerNorm ──
+
+class MessagePassingStep(nn.Module):
+ def __init__(self, latent_dim: int, num_layers: int = 2,
+ activation: str = "leakyrelu"):
+ super().__init__()
+ self.edge_module = EdgeModule(latent_dim, num_layers, activation)
+ self.node_module = NodeModule(latent_dim, num_layers, activation)
+ self.node_ln = nn.LayerNorm(latent_dim)
+ self.edge_ln = nn.LayerNorm(latent_dim)
+
+ def forward(self, graph: Data):
+ old_x = graph.x
+ old_edge = graph.edge_attr
+
+ self.edge_module(graph)
+ graph.edge_attr = self.edge_ln(graph.edge_attr + old_edge)
+
+ self.node_module(graph)
+ graph.x = self.node_ln(graph.x + old_x)
+
+
+# ── Global Virtual Node (uniform mean pooling, attention-gated broadcast) ──
+
+class GlobalVirtualNode(nn.Module):
+ """Simplified GVN: uniform mean pooling → attention-gated broadcast.
+
+ No eta weighting (we don't have residual info at inference).
+ """
+
+ def __init__(self, latent_dim: int):
+ super().__init__()
+ self.gate = nn.Sequential(
+ nn.Linear(2 * latent_dim, latent_dim),
+ nn.LeakyReLU(),
+ nn.Linear(latent_dim, latent_dim),
+ )
+ self.value_proj = nn.Linear(latent_dim, latent_dim)
+ self.scale = nn.Parameter(torch.tensor(0.1))
+
+ def forward(self, graph: Data):
+ batch = getattr(graph, 'batch', None)
+ if batch is None:
+ batch = torch.zeros(graph.x.shape[0], dtype=torch.long,
+ device=graph.x.device)
+
+ # Uniform mean pooling
+ h_V = scatter_mean(graph.x, batch, dim=0) # [B, D]
+
+ # Attention-gated broadcast
+ h_V_exp = h_V[batch] # [N, D]
+ gate_in = torch.cat([graph.x, h_V_exp], dim=-1) # [N, 2D]
+ alpha = torch.sigmoid(self.gate(gate_in)) # [N, D]
+ graph.x = graph.x + self.scale * alpha * self.value_proj(h_V_exp)
+
+
+# ── DensityGNN: full model ──
+
+class DensityGNN(nn.Module):
+ """GNN for supervised final mesh density prediction.
+
+ Architecture:
+ Linear(node_features) → Linear(edge_features)
+ → N × MessagePassingStep (edge/node update + LN + residual)
+ → GlobalVirtualNode (attention-gated global broadcast)
+ → MLP density head → per-node scalar score
+
+ Parameters
+ ----------
+ node_dim : int
+ Input node feature dimension (default 16).
+ edge_dim : int
+ Input edge feature dimension (default 1 for phase_distance).
+ latent_dim : int
+ Hidden dimension for all message passing layers.
+ num_mp_steps : int
+ Number of message passing steps.
+ mlp_layers : int
+ Number of layers in each LatentMLP.
+ head_hidden : int
+ Hidden dimension in the density prediction head.
+ activation : str
+ Activation function name.
+ edge_dropout : float
+ Edge dropout probability during training.
+ """
+
+ def __init__(
+ self,
+ node_dim: int = 16,
+ edge_dim: int = 1,
+ latent_dim: int = 64,
+ num_mp_steps: int = 3,
+ mlp_layers: int = 2,
+ head_hidden: int = 64,
+ activation: str = "leakyrelu",
+ edge_dropout: float = 0.1,
+ ):
+ super().__init__()
+ self.edge_dropout = edge_dropout
+
+ # Embeddings
+ self.node_embedding = nn.Linear(node_dim, latent_dim)
+ self.edge_embedding = nn.Linear(edge_dim, latent_dim)
+
+ # Message passing stack
+ self.mp_steps = nn.ModuleList([
+ MessagePassingStep(latent_dim, mlp_layers, activation)
+ for _ in range(num_mp_steps)
+ ])
+
+ # Global virtual node
+ self.gvn = GlobalVirtualNode(latent_dim)
+
+ # Density head: latent → head_hidden → 1
+ self.head = nn.Sequential(
+ nn.Linear(latent_dim, head_hidden),
+ nn.ReLU(),
+ nn.Linear(head_hidden, 1),
+ )
+
+ def forward(self, graph: Data) -> torch.Tensor:
+ """Forward pass.
+
+ Parameters
+ ----------
+ graph : Data
+ PyG Data with x, edge_index, edge_attr.
+
+ Returns
+ -------
+ pred : (num_nodes,) density score per node.
+ """
+ graph = copy.deepcopy(graph)
+
+ # Edge dropout (training only)
+ if self.edge_dropout > 0 and self.training:
+ graph.edge_index, mask = dropout_edge(
+ graph.edge_index, p=self.edge_dropout, training=True
+ )
+ graph.edge_attr = graph.edge_attr[mask]
+
+ # Embed
+ graph.x = self.node_embedding(graph.x)
+ graph.edge_attr = self.edge_embedding(graph.edge_attr)
+
+ # Message passing
+ for step in self.mp_steps:
+ step(graph)
+
+ # Global broadcast
+ self.gvn(graph)
+
+ # Density head
+ return self.head(graph.x).squeeze(-1)
diff --git a/outlook/src/graph.py b/outlook/src/graph.py
new file mode 100644
index 0000000..32d7133
--- /dev/null
+++ b/outlook/src/graph.py
@@ -0,0 +1,108 @@
+# 将初始网格转为 PyG Data（节点特征、边索引、边特征）。
+"""graph_builder.py — Build PyG graph Data from initial mesh for GNN training.
+
+Constructs node features (16-dim), edge_index (bidirectional + self-loops),
+and edge features (phase_distance) from an initial mesh and physical parameters.
+"""
+
+from typing import Dict
+
+import numpy as np
+import torch
+from torch_geometric.data import Data
+
+from environment.fem_util import get_element_midpoints
+from outlook.src.feat import build_initial_cell_features
+
+
+def build_edge_index_np(mesh) -> np.ndarray:
+ """Build bidirectional + self-loop edge_index from mesh face-to-triangle map.
+
+ Returns (2, n_edges) int64 numpy array. This is the numpy-only version
+ used by gen.py and rollout.py (which don't need torch tensors at this
+ point). graph.py's build_graph_from_mesh wraps the result in a torch
+ tensor.
+ """
+ f2t = mesh.f2t
+ neighbor_mask = f2t[1] != -1
+ neighbors = f2t[:, neighbor_mask]
+
+ n_cells = mesh.t.shape[1]
+ src_fwd = neighbors[0]
+ dst_fwd = neighbors[1]
+ src_bwd = neighbors[1]
+ dst_bwd = neighbors[0]
+ self_ids = np.arange(n_cells)
+
+ src_all = np.concatenate([src_fwd, src_bwd, self_ids])
+ dst_all = np.concatenate([dst_fwd, dst_bwd, self_ids])
+ return np.vstack([src_all, dst_all]).astype(np.int64)
+
+
+def build_graph_from_mesh(mesh, params: Dict, budget_ratio: float) -> Data:
+ """Build a PyG Data object from an initial mesh.
+
+ Parameters
+ ----------
+ mesh : skfem.Mesh
+ Initial mesh with p (2, n_vertices), t (3, n_elements), f2t (2, n_faces).
+ params : dict
+ Physical parameters (k, eps_r, cx, cy, radius).
+ budget_ratio : float
+ Budget ratio conditioning feature (appended as 16th feature).
+
+ Returns
+ -------
+ Data
+ PyG Data with:
+ - x: (n_cells, 16) float32 node features
+ - edge_index: (2, n_edges) long
+ - edge_attr: (n_edges, 1) float32 phase distance
+ """
+ k = params["k"]
+ eps_r = params["eps_r"]
+ cx = params["cx"]
+ cy = params["cy"]
+ radius = params["radius"]
+
+ # ── Node features (16-dim) ──
+ node_features = build_initial_cell_features(mesh, params, budget_ratio)
+ x = torch.tensor(node_features, dtype=torch.float32)
+
+ # ── Element neighbors (bidirectional + self-loops) ──
+ edge_index = torch.tensor(build_edge_index_np(mesh), dtype=torch.long)
+
+ # Need neighbor pairs for edge features
+ f2t = mesh.f2t
+ neighbor_mask = f2t[1] != -1
+ neighbors = f2t[:, neighbor_mask] # (2, N_pairs)
+ src_fwd = neighbors[0]
+ dst_fwd = neighbors[1]
+ n_cells = mesh.t.shape[1]
+
+ # ── Edge features: phase_distance ──
+ midpoints = get_element_midpoints(mesh) # (N, 2)
+
+ eps_r_local = np.where(
+ (midpoints[:, 0] - cx) ** 2 + (midpoints[:, 1] - cy) ** 2 <= radius ** 2,
+ eps_r, 1.0
+ )
+
+ n_pairs = neighbors.shape[1]
+ euclidean_dist = np.linalg.norm(
+ midpoints[dst_fwd] - midpoints[src_fwd], axis=1
+ )
+ k_local_src = k * np.sqrt(np.maximum(eps_r_local[src_fwd], 1.0))
+ k_local_dst = k * np.sqrt(np.maximum(eps_r_local[dst_fwd], 1.0))
+ k_edge = np.sqrt(k_local_src * k_local_dst)
+ phase_dist_fwd = euclidean_dist * k_edge / (2.0 * np.pi)
+
+ # Bidirectional: same features for both directions
+ phase_dist = np.concatenate([
+ phase_dist_fwd, # forward edges
+ phase_dist_fwd, # backward edges (same distance)
+ np.zeros(n_cells), # self-loops
+ ])
+ edge_attr = torch.tensor(phase_dist, dtype=torch.float32).unsqueeze(-1)
+
+ return Data(x=x, edge_index=edge_index, edge_attr=edge_attr)
diff --git a/outlook/src/mesh.py b/outlook/src/mesh.py
new file mode 100644
index 0000000..751c531
--- /dev/null
+++ b/outlook/src/mesh.py
@@ -0,0 +1,183 @@
+# 根据 density score 对初始网格做 top-k 加密，直到接近 target_elements。
+"""mesh_generator.py — Convert network density scores into refined meshes.
+
+Provides score-driven refinement: each initial cell gets a priority score,
+and cells are refined (top-k) until the target element budget is reached.
+"""
+
+import copy
+from typing import Tuple
+
+import numpy as np
+
+
+def generate_mesh_from_density_score(
+ initial_mesh,
+ score: np.ndarray,
+ target_elements: int,
+ strategy: str = "topk",
+) -> Tuple:
+ """Refine the initial mesh according to per-cell density scores.
+
+ Uses iterative top-k refinement: at each step, leaf cells inherit the
+ score of their originating initial cell, and the highest-scored leaves
+ are refined until the target element count is reached.
+
+ Parameters
+ ----------
+ initial_mesh : skfem.Mesh
+ score : (N_init,) float
+ Per-initial-cell density/priority score (higher = refine first).
+ target_elements : int
+ Target total element count.
+ strategy : str
+ Refinement strategy. Currently only "topk" is implemented.
+
+ Returns
+ -------
+ final_mesh : skfem.Mesh
+ n_elements : int
+ Actual element count of the final mesh.
+ n_steps : int
+ Number of refinement iterations performed.
+ """
+ mesh = copy.deepcopy(initial_mesh)
+ n_init = initial_mesh.t.shape[1]
+ leaf_to_initial = np.arange(n_init, dtype=np.int64)
+
+ n_steps = 0
+ max_steps = 50
+
+ while mesh.t.shape[1] < target_elements and n_steps < max_steps:
+ n_current = mesh.t.shape[1]
+ remaining = target_elements - n_current
+
+ # Each refinement produces 4 children from 1 parent, net gain = 3
+ max_to_refine = max(1, remaining // 3)
+ if max_to_refine > n_current:
+ max_to_refine = n_current
+
+ # Leaf scores inherit from their originating initial cell
+ leaf_scores = score[leaf_to_initial]
+
+ if max_to_refine >= n_current:
+ selected = np.arange(n_current)
+ else:
+ score_range = leaf_scores.max() - leaf_scores.min()
+ if score_range < 1e-12:
+ # All scores equal -> uniform spacing
+ selected = np.linspace(0, n_current - 1, max_to_refine, dtype=np.int64)
+ else:
+ selected = np.argpartition(leaf_scores, -max_to_refine)[-max_to_refine:]
+
+ if len(selected) == 0:
+ break
+
+ new_mesh = mesh.refined(selected)
+
+ # Propagate leaf_to_initial mapping via element_finder
+ new_midpoints = np.mean(new_mesh.p[:, new_mesh.t], axis=1).T
+ finder = mesh.element_finder()
+ parent_indices = finder(*new_midpoints.T)
+ parent_indices = np.clip(parent_indices, 0, n_current - 1)
+ leaf_to_initial = leaf_to_initial[parent_indices]
+
+ mesh = new_mesh
+ n_steps += 1
+
+ if mesh.t.shape[1] == n_current:
+ break
+
+ return mesh, mesh.t.shape[1], n_steps
+
+
+def generate_mesh_from_scores(
+ initial_mesh,
+ scores: np.ndarray,
+ target_elements: int,
+ max_steps: int = 50,
+) -> dict:
+ """Refine the initial mesh according to per-cell density scores.
+
+ Like generate_mesh_from_density_score but returns detailed info
+ including overshoot ratio and refine history.
+
+ Parameters
+ ----------
+ initial_mesh : skfem.Mesh
+ scores : (N_init,) float
+ Per-initial-cell density/priority score (higher = refine first).
+ target_elements : int
+ Target total element count (absolute, not ratio).
+ max_steps : int
+ Maximum refinement iterations.
+
+ Returns
+ -------
+ dict with keys:
+ final_mesh : skfem.Mesh
+ actual_elements : int
+ overshoot_ratio : float (actual_elements / target_elements)
+ n_steps : int
+ refine_history : list of dict (elements_before, elements_after, n_selected)
+ """
+ mesh = copy.deepcopy(initial_mesh)
+ n_init = initial_mesh.t.shape[1]
+ leaf_to_initial = np.arange(n_init, dtype=np.int64)
+
+ n_steps = 0
+ refine_history = []
+
+ while mesh.t.shape[1] < target_elements and n_steps < max_steps:
+ n_current = mesh.t.shape[1]
+ remaining = target_elements - n_current
+
+ # Each refinement produces 4 children from 1 parent, net gain = 3
+ max_to_refine = max(1, remaining // 3)
+ if max_to_refine > n_current:
+ max_to_refine = n_current
+
+ # Leaf scores inherit from their originating initial cell
+ leaf_scores = scores[leaf_to_initial]
+
+ if max_to_refine >= n_current:
+ selected = np.arange(n_current)
+ else:
+ score_range = leaf_scores.max() - leaf_scores.min()
+ if score_range < 1e-12:
+ selected = np.linspace(0, n_current - 1, max_to_refine, dtype=np.int64)
+ else:
+ selected = np.argpartition(leaf_scores, -max_to_refine)[-max_to_refine:]
+
+ if len(selected) == 0:
+ break
+
+ new_mesh = mesh.refined(selected)
+
+ # Propagate leaf_to_initial mapping via element_finder
+ new_midpoints = np.mean(new_mesh.p[:, new_mesh.t], axis=1).T
+ finder = mesh.element_finder()
+ parent_indices = finder(*new_midpoints.T)
+ parent_indices = np.clip(parent_indices, 0, n_current - 1)
+ leaf_to_initial = leaf_to_initial[parent_indices]
+
+ refine_history.append({
+ "elements_before": n_current,
+ "elements_after": new_mesh.t.shape[1],
+ "n_selected": len(selected),
+ })
+
+ mesh = new_mesh
+ n_steps += 1
+
+ if mesh.t.shape[1] == n_current:
+ break
+
+ actual = mesh.t.shape[1]
+ return {
+ "final_mesh": mesh,
+ "actual_elements": actual,
+ "overshoot_ratio": actual / target_elements if target_elements > 0 else 0.0,
+ "n_steps": n_steps,
+ "refine_history": refine_history,
+ }
diff --git a/outlook/src/metrics.py b/outlook/src/metrics.py
new file mode 100644
index 0000000..0b5285f
--- /dev/null
+++ b/outlook/src/metrics.py
@@ -0,0 +1,138 @@
+# 计算 FEM 解与 Mie 解析解的误差（aw_rel、max_err）。
+"""metrics.py — Unified evaluation metrics for mesh quality assessment.
+
+Provides Mie-analytical error computation and standardized mesh evaluation.
+"""
+
+import numpy as np
+from typing import Dict, Optional
+
+
+def compute_mie_error(mesh, u_fem: np.ndarray, params: Dict[str, float]) -> Dict[str, float]:
+ """Compute FEM vs Mie analytical solution error.
+
+ Uses area-weighted relative error:
+ aw_rel = sqrt( sum(err_tri^2 * area) / sum(ref_tri^2 * area) )
+
+ Parameters
+ ----------
+ mesh : skfem.Mesh
+ u_fem : (n_vertices,) complex128
+ FEM solution at mesh vertices.
+ params : dict
+ Must contain: k, eps_r, cx, cy, radius
+
+ Returns
+ -------
+ dict with keys: aw_rel, max_err, DoF, n_elements, n_vertices
+ """
+ from environment.mie_solution import mie_scattered_field
+
+ k = params["k"]
+ eps_r = params["eps_r"]
+ cx = params["cx"]
+ cy = params["cy"]
+ radius = params["radius"]
+
+ pts = mesh.p.T # (n_vertices, 2)
+ tri = mesh.t.T # (n_elements, 3)
+
+ u_mie = mie_scattered_field(pts, k0=k, eps_r=eps_r, radius=radius, cx=cx, cy=cy)
+
+ u_fem_scalar = np.real(u_fem)
+ u_mie_scalar = np.real(u_mie)
+
+ err_abs = np.abs(u_fem_scalar - u_mie_scalar)
+ ref_abs = np.abs(u_mie_scalar)
+
+ # Triangle areas
+ v1, v2, v3 = pts[tri[:, 0]], pts[tri[:, 1]], pts[tri[:, 2]]
+ tri_areas = 0.5 * np.abs(
+ (v2[:, 0] - v1[:, 0]) * (v3[:, 1] - v1[:, 1])
+ - (v3[:, 0] - v1[:, 0]) * (v2[:, 1] - v1[:, 1])
+ )
+
+ # Area-weighted error
+ err_tri_sq = (
+ err_abs[tri[:, 0]] ** 2
+ + err_abs[tri[:, 1]] ** 2
+ + err_abs[tri[:, 2]] ** 2
+ ) / 3.0
+ ref_tri_sq = (
+ ref_abs[tri[:, 0]] ** 2
+ + ref_abs[tri[:, 1]] ** 2
+ + ref_abs[tri[:, 2]] ** 2
+ ) / 3.0
+
+ ref_total = np.sum(ref_tri_sq * tri_areas)
+
+ aw_rel = (
+ float(np.sqrt(np.sum(err_tri_sq * tri_areas) / ref_total))
+ if ref_total > 1e-12
+ else float("nan")
+ )
+ max_err = float(np.max(err_abs))
+
+ return {
+ "aw_rel": aw_rel,
+ "max_err": max_err,
+ "DoF": mesh.p.shape[1],
+ "n_elements": mesh.t.shape[1],
+ "n_vertices": mesh.p.shape[1],
+ }
+
+
+def evaluate_mesh(
+ problem,
+ mesh,
+ params: Dict[str, float],
+ teacher_stats: Optional[Dict[str, float]] = None,
+ solve_count: int = 1,
+ eta_count: int = 0,
+) -> Dict[str, float]:
+ """Evaluate a mesh by solving FEM and computing Mie error.
+
+ Parameters
+ ----------
+ problem : HelmholtzProblem
+ mesh : skfem.Mesh
+ params : dict
+ Physical parameters for Mie error.
+ teacher_stats : dict, optional
+ Teacher mesh statistics for computing ratios. Expected keys: elements, dofs.
+ solve_count : int
+ Number of FEM solves used to produce this mesh.
+ eta_count : int
+ Number of residual estimator evaluations used.
+
+ Returns
+ -------
+ dict with standardized fields:
+ aw_rel, max_err, elements, dofs,
+ element_ratio_to_teacher, dof_ratio_to_teacher, num_solves
+ """
+ from skfem import Basis, ElementTriP1
+
+ basis = Basis(mesh, ElementTriP1())
+ u = problem.calculate_solution(basis=basis, cache=False)
+
+ err = compute_mie_error(mesh, u, params)
+
+ result = {
+ "aw_rel": err["aw_rel"],
+ "max_err": err["max_err"],
+ "elements": err["n_elements"],
+ "dofs": err["DoF"],
+ "num_solves": solve_count,
+ }
+
+ if teacher_stats is not None:
+ t_elements = teacher_stats.get("elements", 1)
+ t_dofs = teacher_stats.get("dofs", 1)
+ result["element_ratio_to_teacher"] = err["n_elements"] / max(t_elements, 1)
+ result["dof_ratio_to_teacher"] = err["DoF"] / max(t_dofs, 1)
+ else:
+ result["element_ratio_to_teacher"] = 1.0
+ result["dof_ratio_to_teacher"] = 1.0
+
+ return result
diff --git a/outlook/src/problem.py b/outlook/src/problem.py
new file mode 100644
index 0000000..696f982
--- /dev/null
+++ b/outlook/src/problem.py
@@ -0,0 +1,88 @@
+# 从参数字典创建 Helmholtz 散射问题实例和初始网格。
+"""problem_factory.py — Create Helmholtz cylinder scattering problems from parameter dicts.
+
+Wraps the existing environment backends (helmholtz.py, domain.py) to provide a
+clean interface for the one-shot density prediction pipeline.
+"""
+
+import copy
+import sys
+from pathlib import Path
+from typing import Any, Dict, Optional, Tuple
+
+import numpy as np
+
+_PROJECT_ROOT = Path(__file__).resolve().parent.parent.parent
+if str(_PROJECT_ROOT) not in sys.path:
+ sys.path.insert(0, str(_PROJECT_ROOT))
+
+from environment.helmholtz import HelmholtzProblem
+
+
+def create_problem_from_params(
+ params: Dict[str, float],
+ cfg: Optional[Dict[str, Any]] = None,
+ random_state: Optional[np.random.RandomState] = None,
+) -> Tuple[HelmholtzProblem, "Mesh"]:
+ """Create a HelmholtzProblem and return (problem, initial_mesh).
+
+ Parameters
+ ----------
+ params : dict
+ Must contain: k, eps_r (or epsilon_r), radius, center_x (or cx), center_y (or cy).
+ cfg : dict, optional
+ Override default FEM configuration fields. If None, uses sensible defaults
+ matching the existing experiments (k_ref=6.0, k_exponent=2.0, boundary=[0,0,1,1],
+ initial_num_elements=50).
+ random_state : np.random.RandomState, optional
+ RNG for mesh generation. If None, creates a new one.
+
+ Returns
+ -------
+ problem : HelmholtzProblem
+ initial_mesh : skfem.MeshTri1
+ """
+ # Normalize param keys (accept both naming conventions)
+ k = params.get("k", params.get("wave_number", 10.0))
+ eps_r = params.get("eps_r", params.get("epsilon_r", 2.0))
+ cx = params.get("cx", params.get("center_x", 0.5))
+ cy = params.get("cy", params.get("center_y", 0.5))
+ radius = params.get("radius", 0.2)
+
+ if random_state is None:
+ random_state = np.random.RandomState()
+
+ # Build fem_config with defaults
+ default_cfg = {
+ "helmholtz": {
+ "wave_number": float(k),
+ "wave_number_mode": "fixed",
+ "scatterer": {
+ "mode": "fixed",
+ "cx": float(cx),
+ "cy": float(cy),
+ "radius": float(radius),
+ "eps_r": float(eps_r),
+ },
+ "k_ref": 6.0,
+ "k_exponent": 2.0,
+ },
+ "domain": {
+ "boundary": [0, 0, 1, 1],
+ "initial_num_elements": 50,
+ },
+ }
+
+ # Merge user overrides
+ if cfg is not None:
+ for key in cfg:
+ if key in default_cfg and isinstance(default_cfg[key], dict) and isinstance(cfg[key], dict):
+ default_cfg[key].update(cfg[key])
+ else:
+ default_cfg[key] = cfg[key]
+
+ problem = HelmholtzProblem(
+ fem_config=default_cfg,
+ random_state=random_state,
+ )
+ return problem, problem.initial_mesh
diff --git a/outlook/src/rollout.py b/outlook/src/rollout.py
new file mode 100644
index 0000000..314ae86
--- /dev/null
+++ b/outlook/src/rollout.py
@@ -0,0 +1,863 @@
+#!/usr/bin/env python3
+"""
+rollout.py — Unified AMR rollout for correction GNN evaluation.
+
+Single source of truth for the iterative refinement loop used by:
+ - viz_correction.py (viz_amr, compare plots)
+ - eval_correction.py (rollout evaluation)
+
+Two-phase design:
+ 1. build_physics_safe_initial_mesh() (gen.py)
+ Uses score = max_edge / h_target; refines cells with score > 1
+ until all are physics-safe or max_initial_elements reached.
+
+ 2. run_rollout_to_budget() (this file)
+ Budget-aware top-k refinement to target_elements.
+ No score-based stopping — always reaches the target budget.
+
+All callers share the same:
+ - score computation (physics / neural / hybrid / eta)
+ - top-k cell selection
+ - area safety filter
+ - budget-aware binary search truncation
+ - FEM validation (strict mode)
+ - actual_elements recording
+
+Usage:
+ from outlook.src.rollout import run_rollout_to_budget, compute_scores
+
+ result = run_rollout_to_budget(
+ method="physics",
+ params={"k": 10, "eps_r": 4, "cx": 0.5, "cy": 0.5, "radius": 0.15},
+ target_elements=6000,
+ budget_mode="strict",
+ save_steps=True,
+ )
+"""
+
+import copy
+from typing import Optional
+
+import numpy as np
+
+
+# ============================================================================
+# GNN inference (internal)
+# ============================================================================
+
+
+def _predict_gnn(model, normalizer: dict, mesh, params: dict,
+ device: str = "cpu") -> np.ndarray:
+ """Return per-cell GNN sigmoid probabilities (raw, no top-k)."""
+ import torch
+ from torch_geometric.data import Data
+ from outlook.src.train_correction import CorrectionGNN, compute_edge_attr
+ from outlook.src.feat import build_initial_cell_features
+ from outlook.src.graph import build_edge_index_np
+ from outlook.src.gen import compute_physics_score
+
+ features = build_initial_cell_features(mesh, params)[:, :15]
+ physics_score = compute_physics_score(mesh, params)
+ x_np = np.concatenate([features, physics_score[:, None]], axis=1).astype(np.float32)
+
+ mean = np.array(normalizer["mean"], dtype=np.float32)
+ scale = np.array(normalizer["scale"], dtype=np.float32)
+ x_norm = (x_np - mean) / scale
+
+ x = torch.tensor(x_norm, dtype=torch.float32)
+ edge_index = torch.tensor(build_edge_index_np(mesh), dtype=torch.long)
+ edge_attr = compute_edge_attr(x, edge_index)
+ graph = Data(x=x, edge_index=edge_index, edge_attr=edge_attr).to(device)
+
+ with torch.no_grad():
+ logits = model(graph).cpu().numpy().flatten()
+ return 1.0 / (1.0 + np.exp(-logits))
+
+
+# ============================================================================
+# Score computation (unified)
+# ============================================================================
+
+
+def compute_scores(
+ method: str,
+ mesh,
+ params: dict,
+ model=None,
+ normalizer: dict = None,
+ device: str = "cpu",
+ alpha: float = 0.5,
+ beta: float = 0.5,
+ q: float = 2.0,
+) -> np.ndarray:
+ """Return per-cell scores for refinement marking.
+
+ Methods
+ -------
+ physics : max_edge / h_target (h_target = lambda_eff / q)
+ neural : GNN sigmoid probability
+ hybrid : alpha * zscore(physics) + beta * zscore(neural)
+ eta : residual indicator (requires FEM solve)
+ """
+ from outlook.src.gen import compute_physics_score
+
+ if method == "physics":
+ return compute_physics_score(mesh, params, q=q)
+
+ elif method == "neural":
+ return _predict_gnn(model, normalizer, mesh, params, device)
+
+ elif method == "hybrid":
+ physics = compute_physics_score(mesh, params, q=q)
+ neural = _predict_gnn(model, normalizer, mesh, params, device)
+ p_std = float(physics.std())
+ n_std = float(neural.std())
+ p_z = (physics - physics.mean()) / p_std if p_std > 1e-12 else np.zeros_like(physics)
+ n_z = (neural - neural.mean()) / n_std if n_std > 1e-12 else np.zeros_like(neural)
+ return alpha * p_z + beta * n_z
+
+ elif method == "eta":
+ from skfem import Basis, ElementTriP1
+ from environment.helmholtz import (
+ HelmholtzProblem,
+ _compute_eps_r_at_midpoints,
+ _compute_residual_indicator,
+ )
+ from outlook.src.gen import make_fem_config
+
+ fem_config = make_fem_config(params)
+ problem = HelmholtzProblem(
+ fem_config=fem_config,
+ random_state=np.random.RandomState(42),
+ )
+ basis = Basis(mesh, ElementTriP1())
+ u = problem.calculate_solution(basis=basis, cache=False)
+ eps_r_arr = _compute_eps_r_at_midpoints(
+ mesh, cx=params["cx"], cy=params["cy"],
+ radius=params["radius"], eps_r_in=params["eps_r"],
+ )
+ return _compute_residual_indicator(mesh, u, k=params["k"], eps_r=eps_r_arr)
+
+ else:
+ raise ValueError(f"Unknown method: {method!r}")
+
+
+# ============================================================================
+# Model loading
+# ============================================================================
+
+
+def load_model(checkpoint_path: str, device: str = "cpu"):
+ """Load correction GNN + normalizer from checkpoint."""
+ import torch
+ from outlook.src.train_correction import CorrectionGNN
+
+ ckpt = torch.load(checkpoint_path, map_location=device, weights_only=False)
+ config = ckpt["config"]
+ normalizer = ckpt["normalizer"]
+
+ model = CorrectionGNN(
+ node_dim=config["node_dim"],
+ edge_dim=config["edge_dim"],
+ latent_dim=config["latent_dim"],
+ num_mp_steps=config["num_mp_steps"],
+ head_hidden=config["head_hidden"],
+ edge_dropout=0.0,
+ )
+ model.load_state_dict(ckpt["model_state_dict"])
+ model.eval()
+ model.to(device)
+ return model, normalizer, config
+
+
+# ============================================================================
+# Shared AMR refinement: area-safety + reverse-Dorfler + top-k by log(eta)
+# ============================================================================
+
+
+def _area_eligible(mesh) -> np.ndarray:
+ """Return indices of cells with area > 1e-10 (non-degenerate)."""
+ i0, i1, i2 = mesh.t[0], mesh.t[1], mesh.t[2]
+ det_J = (
+ (mesh.p[0, i1] - mesh.p[0, i0]) * (mesh.p[1, i2] - mesh.p[1, i0])
+ - (mesh.p[0, i2] - mesh.p[0, i0]) * (mesh.p[1, i1] - mesh.p[1, i0])
+ )
+ areas = np.abs(det_J) / 2.0
+ return np.where(areas > 1e-10)[0]
+
+
+def _refine_by_eta(mesh, eta, mark_fraction, max_elements):
+ """Shared refinement step: area-safety + reverse-Dorfler + top-k by log(eta).
+
+ Implements the same refinement logic used by gen.py, amr.py, and
+ viz_correction.py. Returns the refined mesh, or None if no eligible
+ cells remain or the budget is already reached.
+
+ Parameters
+ ----------
+ mesh : skfem.Mesh
+ Current mesh.
+ eta : (n_elem,) array
+ Per-cell residual indicator.
+ mark_fraction : float
+ Fraction of elements to refine per step.
+ max_elements : int
+ Hard cap on element count.
+
+ Returns
+ -------
+ mesh or None
+ Refined mesh, or None if refinement is not possible.
+ """
+ n_elem = mesh.t.shape[1]
+ if n_elem >= max_elements:
+ return None
+
+ # 1. Area safety filter
+ area_eligible = _area_eligible(mesh)
+
+ # 2. Reverse Dorfler: remove lowest-error cells
+ eta_sq = eta ** 2
+ total_energy = np.sum(eta_sq)
+ if total_energy > 0 and len(area_eligible) > 1:
+ idx_asc = np.argsort(eta)
+ cumsum_asc = np.cumsum(eta_sq[idx_asc])
+ k_dorfler = int(np.searchsorted(cumsum_asc, 0.01 * total_energy))
+ min_keep = max(1, n_elem // 5)
+ k_cut = min(k_dorfler, n_elem - min_keep)
+ error_eligible = idx_asc[k_cut:]
+ else:
+ error_eligible = np.arange(n_elem)
+
+ eligible = np.intersect1d(area_eligible, error_eligible)
+ if len(eligible) == 0:
+ return None
+
+ # 3. Top-k by log(eta)
+ log_eta = np.log(np.maximum(eta, 1e-30))
+ n_select = min(
+ len(eligible),
+ max(1, int(n_elem * mark_fraction)),
+ (max_elements - n_elem) // 4,
+ )
+ if n_select <= 0:
+ return None
+
+ selected = eligible[np.argsort(log_eta[eligible])[-n_select:]]
+ return mesh.refined(selected)
+
+
+# ============================================================================
+# Budget-aware refinement (strict mode)
+# ============================================================================
+
+
+def _choose_budgeted_refinement(mesh, eligible_indices, scores, target,
+ n_mark=None, validate_solve=False, problem=None,
+ params=None):
+ """Binary search for the largest refinement batch that stays within budget.
+
+ Searches within the top-n_mark cells (by score) of eligible_indices.
+ Uses physical tie-breaking when many cells share the same cutoff score.
+
+ Parameters
+ ----------
+ mesh : current mesh
+ eligible_indices : cell indices eligible for refinement (after area safety)
+ scores : per-cell scores (higher = refine first)
+ target : max element count
+ n_mark : int, optional
+ Max number of cells to consider. Default: len(eligible_indices).
+ validate_solve : if True, check that refined mesh produces valid FEM
+ problem : HelmholtzProblem (required if validate_solve=True)
+ params : dict, optional — physical params for tie-breaking
+
+ Returns
+ -------
+ refined_mesh or None if no valid refinement found
+ """
+ from skfem import Basis, ElementTriP1
+
+ # Sort eligible cells by score descending with physical tie-breaking
+ if params is not None:
+ p = mesh.p
+ t = mesh.t
+ mx = (p[0, t[0]] + p[0, t[1]] + p[0, t[2]]) / 3.0
+ my = (p[1, t[0]] + p[1, t[1]] + p[1, t[2]]) / 3.0
+ cx, cy, radius = params["cx"], params["cy"], params["radius"]
+ dist = np.sqrt((mx - cx)**2 + (my - cy)**2)
+ signed_dist = dist - radius
+ is_inside = dist <= radius
+ domain_center = np.array([
+ (p[0].min() + p[0].max()) / 2.0,
+ (p[1].min() + p[1].max()) / 2.0,
+ ])
+ k = min(n_mark or len(eligible_indices), len(eligible_indices))
+ sorted_eligible, _ = _topk_indices(
+ scores[eligible_indices], k,
+ signed_dist[eligible_indices],
+ is_inside[eligible_indices],
+ domain_center,
+ )
+ sorted_eligible = eligible_indices[sorted_eligible]
+ else:
+ order = np.argsort(scores[eligible_indices])[::-1]
+ sorted_eligible = eligible_indices[order]
+ # Limit to top-n_mark
+ if n_mark is not None and n_mark < len(sorted_eligible):
+ sorted_eligible = sorted_eligible[:n_mark]
+
+ n_cells = mesh.t.shape[1]
+ if n_cells >= target:
+ return None
+
+ lo, hi = 1, len(sorted_eligible)
+ best_n = 0
+ best_mesh = None
+
+ while lo <= hi:
+ mid = (lo + hi) // 2
+ selected = sorted_eligible[:mid]
+ trial = mesh.refined(selected)
+
+ if trial.t.shape[1] > target:
+ hi = mid - 1
+ continue
+
+ if validate_solve and problem is not None:
+ try:
+ b_trial = Basis(trial, ElementTriP1())
+ u_trial = problem.calculate_solution(basis=b_trial, cache=False)
+ if np.any(np.isnan(u_trial)):
+ hi = mid - 1
+ continue
+ except Exception:
+ hi = mid - 1
+ continue
+
+ best_n = mid
+ best_mesh = trial
+ lo = mid + 1
+
+ if best_n == 0:
+ # Even 1 cell overshoots — try single cell
+ trial = mesh.refined(sorted_eligible[:1])
+ if trial.t.shape[1] <= target:
+ if validate_solve and problem is not None:
+ try:
+ b_trial = Basis(trial, ElementTriP1())
+ u_trial = problem.calculate_solution(basis=b_trial, cache=False)
+ if not np.any(np.isnan(u_trial)):
+ return trial
+ except Exception:
+ pass
+ else:
+ return trial
+ return None
+
+ return best_mesh
+
+
+# ============================================================================
+# Score diagnostics
+# ============================================================================
+
+
+def _compute_cell_geometry(mesh, params):
+ """Compute per-cell midpoints, signed_dist, is_inside, and domain_center once.
+
+ Returns a dict with keys: mx, my, signed_dist, is_inside, domain_center.
+ Callers can reuse these instead of recomputing from scratch.
+ """
+ cx, cy, radius = params["cx"], params["cy"], params["radius"]
+ p = mesh.p
+ t = mesh.t
+ mx = (p[0, t[0]] + p[0, t[1]] + p[0, t[2]]) / 3.0
+ my = (p[1, t[0]] + p[1, t[1]] + p[1, t[2]]) / 3.0
+ dist = np.sqrt((mx - cx)**2 + (my - cy)**2)
+ return {
+ "mx": mx, "my": my,
+ "signed_dist": dist - radius,
+ "is_inside": dist <= radius,
+ "domain_center": np.array([(p[0].min() + p[0].max()) / 2.0,
+ (p[1].min() + p[1].max()) / 2.0]),
+ }
+
+
+def _compute_score_diagnostics(scores, mesh, params, selected=None, geom=None):
+ """Compute per-step score diagnostics for logging.
+
+ Parameters
+ ----------
+ scores : (n_cells,) array
+ mesh : current mesh
+ params : dict with k, eps_r, cx, cy, radius
+ selected : array of selected cell indices, or None
+ geom : dict from _compute_cell_geometry, optional (avoids recomputation)
+
+ Returns
+ -------
+ dict with score statistics and cell classification
+ """
+ if geom is None:
+ geom = _compute_cell_geometry(mesh, params)
+ mx, my = geom["mx"], geom["my"]
+ inside = geom["is_inside"]
+ dist = np.sqrt((mx - params["cx"])**2 + (my - params["cy"])**2)
+
+ # Interface band: within one h_target of boundary
+ k = params["k"]
+ eps_r_val = params["eps_r"]
+ lambda_eff_in = 2.0 * np.pi / (k * np.sqrt(eps_r_val))
+ lambda_eff_out = 2.0 * np.pi / k
+ h_target_in = lambda_eff_in / 2.0
+ h_target_out = lambda_eff_out / 2.0
+ margin = np.where(inside, h_target_in, h_target_out)
+ interface = (dist > params["radius"]) & (dist <= params["radius"] + margin)
+ outside = dist > params["radius"] + margin
+
+ diag = {
+ "score_max": float(np.max(scores)),
+ "score_mean": float(np.mean(scores)),
+ "score_p50": float(np.percentile(scores, 50)),
+ "score_p90": float(np.percentile(scores, 90)),
+ "fraction_gt1": float(np.mean(scores > 1.0)),
+ "n_inside": int(np.sum(inside)),
+ "n_interface": int(np.sum(interface)),
+ "n_outside": int(np.sum(outside)),
+ }
+
+ if selected is not None and len(selected) > 0:
+ sel_inside = int(np.sum(inside[selected]))
+ sel_interface = int(np.sum(interface[selected]))
+ sel_outside = int(np.sum(outside[selected]))
+ n_sel = len(selected)
+ diag["selected_inside_frac"] = sel_inside / n_sel
+ diag["selected_interface_frac"] = sel_interface / n_sel
+ diag["selected_outside_frac"] = sel_outside / n_sel
+ sx = mx[selected]
+ sy = my[selected]
+ diag["selected_x_range"] = float(sx.max() - sx.min())
+ diag["selected_y_range"] = float(sy.max() - sy.min())
+ else:
+ diag["selected_inside_frac"] = 0.0
+ diag["selected_interface_frac"] = 0.0
+ diag["selected_outside_frac"] = 0.0
+ diag["selected_x_range"] = 0.0
+ diag["selected_y_range"] = 0.0
+
+ return diag
+
+
+# ============================================================================
+# Deterministic top-k selection with physical tie-breaking
+# ============================================================================
+
+
+def _topk_indices(scores, k, signed_dist, is_inside, domain_center):
+ """Select top-k cell indices by score with deterministic physical tie-breaking.
+
+ When many cells share the same cutoff score (common on uniform/graded
+ meshes), raw argsort selects by array index — spatially arbitrary.
+ This function breaks ties using physical criteria to produce a
+ spatially coherent, deterministic selection.
+
+ Parameters
+ ----------
+ scores : (n_cells,) array — higher = refine first
+ k : int — number of cells to select
+ signed_dist : (n_cells,) array — negative inside scatterer, positive outside
+ is_inside : (n_cells,) bool array — True if cell midpoint is inside scatterer
+ domain_center : (2,) array — [cx, cy] of domain for spatial tie-breaking
+
+ Returns
+ -------
+ topk_idx : (k,) int array — selected cell indices
+ diag : dict with cutoff_score, num_tied_at_cutoff
+ """
+ n = len(scores)
+ k = min(k, n)
+
+ # Partition top-k (O(n), no full sort needed)
+ topk_idx = np.argpartition(scores, -k)[-k:]
+ # Sort top-k by score descending
+ topk_sorted = topk_idx[np.argsort(scores[topk_idx])[::-1]]
+
+ # Check for ties at the cutoff
+ cutoff_score = float(scores[topk_sorted[-1]])
+ num_tied = int(np.sum(scores == cutoff_score))
+
+ diag = {
+ "cutoff_score": cutoff_score,
+ "num_tied_at_cutoff": num_tied,
+ }
+
+ if num_tied <= 1:
+ # No ties — standard sort is deterministic
+ return topk_sorted, diag
+
+ # ── Physical tie-breaking for cells at cutoff score ──
+ tied_mask = (scores == cutoff_score)
+ tied_idx = np.where(tied_mask)[0]
+
+ # Determine which tied cells are in the top-k and which are not
+ # Those already in topk_sorted stay; those not in may replace
+ # some that are. We re-rank ALL tied cells together.
+ in_topk = np.isin(tied_idx, topk_sorted)
+ # Tied cells currently in top-k (to be re-ranked)
+ tied_in_topk = tied_idx[in_topk]
+ # Tied cells NOT in top-k (candidates to replace those dropped)
+ tied_not_in_topk = tied_idx[~in_topk]
+
+ # How many tied cells should be in the final top-k?
+ n_from_above = k - len(tied_in_topk) # cells with score > cutoff already selected
+ # The above count is: total top-k minus tied-in-topk
+ # But we need to count cells in topk_sorted with score > cutoff
+ n_above_cutoff = int(np.sum(scores[topk_sorted] > cutoff_score))
+ n_tied_needed = k - n_above_cutoff
+
+ if n_tied_needed <= 0:
+ return topk_sorted, diag
+
+ # Combine all tied cells and re-rank by physical criteria
+ all_tied = tied_idx
+ sd = signed_dist[all_tied]
+ inside = is_inside[all_tied].astype(np.float32)
+
+ # Physical tie-breaker priority:
+ # 1. Interface proximity: -abs(signed_dist) → boundary cells first
+ # 2. Inside preference: is_inside → scatterer interior preferred
+ # 3. Spatial uniformity: -dist_to_center → spread selection across domain
+ # (prevents clustering in one corner)
+ dc_x = domain_center[0]
+ dc_y = domain_center[1]
+ # Cell midpoints from signed_dist: we approximate dist_to_center
+ # from the domain center. For cells at the same score, we want
+ # spatial spread, so we use a deterministic spatial key instead
+ # of Euclidean distance (which would cluster at center).
+ # Use: quadrant-based spatial key + distance as final tie-breaker.
+ #
+ # Actually, for spatial spread we want cells FARTHER from center
+ # to also be selected (not just closest). Use signed_dist as the
+ # primary physical key, and cell index as absolute last resort
+ # (it's deterministic even if not spatially meaningful).
+ abs_sd = np.abs(sd)
+ tie_key = (
+ -abs_sd * 1000.0 # interface proximity (highest priority)
+ + inside * 100.0 # inside preference
+ )
+ tied_order = np.argsort(tie_key)[::-1] # descending: best first
+ best_tied = all_tied[tied_order[:n_tied_needed]]
+
+ # Build final selection: non-tied top cells + best tied cells
+ non_tied_in_topk = topk_sorted[scores[topk_sorted] > cutoff_score]
+ result = np.concatenate([non_tied_in_topk, best_tied])
+ return result, diag
+
+
+# ============================================================================
+# Unified AMR rollout
+# ============================================================================
+
+
+def run_rollout_to_budget(
+ method: str,
+ params: dict,
+ target_elements: int,
+ q: float = 2.0,
+ mark_fraction: float = 0.03,
+ max_steps: int = 40,
+ checkpoint_path: str = None,
+ model=None,
+ normalizer: dict = None,
+ device: str = "cpu",
+ seed: int = 42,
+ alpha: float = 0.5,
+ beta: float = 0.5,
+ budget_mode: str = "strict",
+ save_steps: bool = False,
+ verbose: bool = False,
+) -> dict:
+ """Run iterative AMR refinement to target_elements (budget-aware).
+
+ This is the *rollout-to-budget* phase — distinct from initial mesh
+ generation (build_physics_safe_initial_mesh). No score-based stopping:
+ always refines top-k cells by score until target_elements reached.
+
+ Parameters
+ ----------
+ method : str
+ Scoring method: "physics", "neural", "hybrid", or "eta".
+ params : dict
+ Physical parameters (k, eps_r, cx, cy, radius).
+ target_elements : int
+ Target element count (hard cap in strict mode).
+ q : float
+ Elements per wavelength for initial mesh.
+ mark_fraction : float
+ Fraction of cells to mark per step.
+ max_steps : int
+ Maximum refinement iterations.
+ checkpoint_path : str, optional
+ Path to correction GNN checkpoint. Required for neural/hybrid.
+ model : loaded model, optional
+ Pre-loaded model (overrides checkpoint_path).
+ normalizer : dict, optional
+ Pre-loaded normalizer (overrides checkpoint_path).
+ device : str
+ Torch device.
+ seed : int
+ Random seed for problem initialization.
+ alpha, beta : float
+ Weights for hybrid method.
+ budget_mode : str
+ "strict": binary search + area safety + FEM validation. Never exceeds target.
+ "fast": simple min-cap, no area safety, no FEM validation.
+ save_steps : bool
+ If True, record per-step mesh/solution/error for visualization.
+ verbose : bool
+ If True, print per-step progress.
+
+ Returns
+ -------
+ dict with keys:
+ mesh, u_scat, aw_rel, max_err, actual_elements,
+ num_steps, num_solves, steps (if save_steps), score_stats
+ """
+ from skfem import Basis, ElementTriP1
+ from environment.helmholtz import HelmholtzProblem
+ from outlook.src.gen import make_fem_config, build_physics_safe_initial_mesh
+ from outlook.src.metrics import compute_mie_error
+
+ # ── Load model if needed ──
+ if method in ("neural", "hybrid") and model is None:
+ if checkpoint_path is None:
+ raise ValueError(f"method={method!r} requires checkpoint_path or pre-loaded model")
+ model, normalizer, _ = load_model(checkpoint_path, device)
+
+ # ── Create problem and initial mesh ──
+ fem_config = make_fem_config(params)
+ problem = HelmholtzProblem(
+ fem_config=fem_config,
+ random_state=np.random.RandomState(seed),
+ )
+ mesh = build_physics_safe_initial_mesh(params, q=q, verbose=False)
+
+ # Auto-reduce q if initial mesh already exceeds budget
+ while mesh.t.shape[1] >= target_elements and q > 1.0:
+ q_old = q
+ q = round(q - 0.5, 1)
+ if verbose:
+ print(f"[Rollout] Initial mesh ({mesh.t.shape[1]} elem) >= target ({target_elements}), "
+ f"reducing q {q_old} -> {q}")
+ mesh = build_physics_safe_initial_mesh(params, q=q, verbose=False)
+
+ if verbose:
+ print(f"[Rollout] method={method} target={target_elements} "
+ f"budget_mode={budget_mode} mark_fraction={mark_fraction}")
+ print(f"[Rollout] k={params['k']:.2f} eps_r={params['eps_r']:.2f} "
+ f"cx={params['cx']:.2f} cy={params['cy']:.2f} r={params['radius']:.3f}")
+
+ # ── Iterative refinement ──
+ num_steps = 0
+ num_solves = 0
+ steps_data = [] if save_steps else None
+ score_stats = []
+ mesh_was_refined = False
+ prev_score_mean = None
+
+ for step in range(max_steps):
+ n_elem = mesh.t.shape[1]
+ if n_elem >= target_elements:
+ break
+
+ # Optional: FEM solve for step recording
+ u_scat = None
+ if save_steps:
+ basis = Basis(mesh, ElementTriP1())
+ u_scat = problem.calculate_solution(basis=basis, cache=False)
+ num_solves += 1
+
+ if not np.any(np.isnan(u_scat)):
+ err = compute_mie_error(mesh, u_scat, params)
+ if verbose:
+ print(f" Step {step:2d}: elem={n_elem:6d} "
+ f"aw_rel={err['aw_rel']*100:.2f}% max_err={err['max_err']:.4f}")
+ steps_data.append({
+ "mesh": copy.deepcopy(mesh),
+ "u_scat": u_scat.copy(),
+ "aw_rel": err["aw_rel"],
+ "max_err": err["max_err"],
+ "n_elem": n_elem,
+ })
+ else:
+ if verbose:
+ print(f" Step {step:2d}: elem={n_elem:6d} SOLVE FAILED (NaN)")
+
+ # Compute scores
+ scores = compute_scores(
+ method, mesh, params,
+ model=model, normalizer=normalizer,
+ device=device, alpha=alpha, beta=beta, q=q,
+ )
+
+ # ── Compute cell geometry once per step ──
+ geom = _compute_cell_geometry(mesh, params)
+
+ # ── Score diagnostics (before refinement) ──
+ diag = _compute_score_diagnostics(scores, mesh, params, geom=geom)
+ diag["step"] = step
+ diag["n_elem"] = n_elem
+ diag["target_elements"] = target_elements
+ diag["gap"] = target_elements - n_elem
+
+ if budget_mode == "strict":
+ # ── Strict: area safety + binary search ──
+ eligible = _area_eligible(mesh)
+ if len(eligible) == 0:
+ if verbose:
+ print(f" No eligible cells, stopping.")
+ score_stats.append(diag)
+ mesh_was_refined = False
+ break
+
+ n_mark = max(1, int(n_elem * mark_fraction))
+ n_mark = min(n_mark, len(eligible))
+
+ # Snapshot: mesh.refined() in the binary search may corrupt
+ # cached facets/t2f of the original mesh object.
+ mesh_snapshot = copy.deepcopy(mesh)
+
+ refined = _choose_budgeted_refinement(
+ mesh_snapshot, eligible, scores, target_elements,
+ n_mark=n_mark,
+ validate_solve=False,
+ problem=problem,
+ params=params,
+ )
+
+ if refined is None:
+ score_stats.append(diag)
+ mesh_was_refined = False
+ break
+
+ if refined.t.shape[1] <= n_elem:
+ score_stats.append(diag)
+ mesh_was_refined = False
+ break
+
+ # Record selected cells for diagnostics
+ sel_idx, tie_diag = _topk_indices(
+ scores[eligible], n_mark,
+ geom["signed_dist"][eligible],
+ geom["is_inside"][eligible],
+ geom["domain_center"],
+ )
+ selected = eligible[sel_idx]
+ diag_sel = _compute_score_diagnostics(scores, mesh, params, selected, geom=geom)
+ diag["selected_inside_frac"] = diag_sel["selected_inside_frac"]
+ diag["selected_interface_frac"] = diag_sel["selected_interface_frac"]
+ diag["selected_outside_frac"] = diag_sel["selected_outside_frac"]
+ diag["selected_x_range"] = diag_sel["selected_x_range"]
+ diag["selected_y_range"] = diag_sel["selected_y_range"]
+ diag["cutoff_score"] = tie_diag["cutoff_score"]
+ diag["num_tied_at_cutoff"] = tie_diag["num_tied_at_cutoff"]
+
+ mesh = refined
+ mesh_was_refined = True
+
+ else:
+ # ── Fast: simple min-cap ──
+ n_mark = max(1, int(n_elem * mark_fraction))
+ n_mark = min(n_mark, max(1, (target_elements - n_elem) // 3))
+
+ if n_mark >= n_elem:
+ selected = np.arange(n_elem)
+ diag["cutoff_score"] = float(np.min(scores))
+ diag["num_tied_at_cutoff"] = int(np.sum(scores == diag["cutoff_score"]))
+ else:
+ sel_idx, tie_diag = _topk_indices(
+ scores, n_mark,
+ geom["signed_dist"],
+ geom["is_inside"],
+ geom["domain_center"],
+ )
+ selected = sel_idx
+ diag["cutoff_score"] = tie_diag["cutoff_score"]
+ diag["num_tied_at_cutoff"] = tie_diag["num_tied_at_cutoff"]
+
+ # Record selected cells for diagnostics
+ diag_sel = _compute_score_diagnostics(scores, mesh, params, selected, geom=geom)
+ diag["selected_inside_frac"] = diag_sel["selected_inside_frac"]
+ diag["selected_interface_frac"] = diag_sel["selected_interface_frac"]
+ diag["selected_outside_frac"] = diag_sel["selected_outside_frac"]
+ diag["selected_x_range"] = diag_sel["selected_x_range"]
+ diag["selected_y_range"] = diag_sel["selected_y_range"]
+
+ new_mesh = mesh.refined(selected)
+ if new_mesh.t.shape[1] <= n_elem:
+ score_stats.append(diag)
+ mesh_was_refined = False
+ break
+
+ mesh = new_mesh
+ mesh_was_refined = True
+
+ # ── Score decrease tracking ──
+ if prev_score_mean is not None:
+ diag["score_decreased"] = diag["score_mean"] < prev_score_mean
+ else:
+ diag["score_decreased"] = None
+ prev_score_mean = diag["score_mean"]
+
+ score_stats.append(diag)
+
+ # score diagnostics recorded in diag; no per-step print (too noisy)
+
+ num_steps += 1
+
+ # ── Final FEM solve (always — callers need u_scat) ──
+ basis = Basis(mesh, ElementTriP1())
+ u_final = problem.calculate_solution(basis=basis, cache=False)
+ num_solves += 1
+
+ aw_rel = float("nan")
+ max_err = float("nan")
+
+ if not np.any(np.isnan(u_final)):
+ err = compute_mie_error(mesh, u_final, params)
+ aw_rel = err["aw_rel"]
+ max_err = err["max_err"]
+
+ if verbose:
+ print(f" Final: elem={mesh.t.shape[1]:6d} "
+ f"aw_rel={aw_rel*100:.2f}% max_err={max_err:.4f}")
+
+ if save_steps:
+ steps_data.append({
+ "mesh": copy.deepcopy(mesh),
+ "u_scat": u_final.copy(),
+ "aw_rel": aw_rel,
+ "max_err": max_err,
+ "n_elem": mesh.t.shape[1],
+ })
+
+ result = {
+ "mesh": mesh,
+ "u_scat": u_final,
+ "aw_rel": aw_rel,
+ "max_err": max_err,
+ "actual_elements": mesh.t.shape[1],
+ "num_steps": num_steps,
+ "num_solves": num_solves,
+ "score_stats": score_stats,
+ }
+
+ if save_steps:
+ result["steps"] = steps_data
+
+ return result
+
+
+# Backward-compatible alias
+run_rollout = run_rollout_to_budget
diff --git a/outlook/src/test_correction.py b/outlook/src/test_correction.py
new file mode 100644
index 0000000..32863ab
--- /dev/null
+++ b/outlook/src/test_correction.py
@@ -0,0 +1,344 @@
+#!/usr/bin/env python3
+"""
+test_correction.py
+==================
+Evaluate trained correction GNN on validation set.
+
+Outputs:
+ - Per-graph metrics (top-k overlap, AUC)
+ - Comparison: GNN vs physics baseline
+ - Visualization: mesh with predicted vs true teacher_mark cells
+
+Usage:
+ python outlook/src/test_correction.py \
+ --checkpoint outlook/ckpt/correction.pt \
+ --data-dir outlook/data_correction \
+ --device cpu \
+ --visualize
+"""
+
+import argparse
+import glob
+import json
+import re
+import sys
+from pathlib import Path
+from typing import Dict, List
+
+import numpy as np
+
+_PROJECT_ROOT = Path(__file__).resolve().parent.parent.parent
+sys.path.insert(0, str(_PROJECT_ROOT))
+
+import torch
+from torch_geometric.data import Data
+from torch_geometric.loader import DataLoader
+from sklearn.metrics import roc_auc_score
+
+from outlook.src.train_correction import CorrectionGNN, compute_edge_attr, load_correction_dataset
+
+
+# ============================================================================
+# Evaluation
+# ============================================================================
+
+
+def evaluate(
+ model: CorrectionGNN,
+ graphs: List[Data],
+ device: str = "cpu",
+) -> Dict:
+ """Evaluate model on a list of graphs.
+
+ Returns per-graph and overall metrics.
+ """
+ model.eval()
+ model.to(device)
+
+ loader = DataLoader(graphs, batch_size=1, shuffle=False)
+
+ results = []
+ all_logits, all_targets, all_physics = [], [], []
+
+ with torch.no_grad():
+ for i, batch in enumerate(loader):
+ batch = batch.to(device)
+ logits = model(batch).cpu().numpy().flatten()
+ targets = batch.y.cpu().numpy().flatten()
+ g = graphs[i]
+
+ # Physics baseline
+ physics = g.physics_score_raw.numpy()
+
+ # Top-k overlap
+ k = int(targets.sum())
+ if k > 0 and k < len(targets):
+ # GNN
+ top_gnn = set(np.argsort(logits)[-k:])
+ top_true = set(np.where(targets > 0.5)[0])
+ gnn_overlap = len(top_gnn & top_true) / k
+
+ # Physics
+ top_phys = set(np.argsort(physics)[-k:])
+ phys_overlap = len(top_phys & top_true) / k
+ else:
+ gnn_overlap = 0.0
+ phys_overlap = 0.0
+
+ results.append({
+ "file": g.file,
+ "sample_id": g.sample_id,
+ "n_cells": len(targets),
+ "n_positive": k,
+ "gnn_topk": gnn_overlap,
+ "physics_topk": phys_overlap,
+ "gnn_beats_physics": gnn_overlap > phys_overlap,
+ })
+
+ all_logits.append(logits)
+ all_targets.append(targets)
+ all_physics.append(physics)
+
+ # Overall metrics
+ all_logits_cat = np.concatenate(all_logits)
+ all_targets_cat = np.concatenate(all_targets)
+ all_physics_cat = np.concatenate(all_physics)
+
+ try:
+ auc_gnn = roc_auc_score(all_targets_cat, all_logits_cat)
+ except ValueError:
+ auc_gnn = 0.0
+
+ try:
+ auc_phys = roc_auc_score(all_physics_cat, all_targets_cat)
+ except ValueError:
+ auc_phys = 0.0
+
+ gnn_topk_mean = np.mean([r["gnn_topk"] for r in results])
+ phys_topk_mean = np.mean([r["physics_topk"] for r in results])
+ n_beat = sum(1 for r in results if r["gnn_beats_physics"])
+
+ summary = {
+ "n_graphs": len(results),
+ "gnn_auc": float(auc_gnn),
+ "physics_auc": float(auc_phys),
+ "gnn_topk_mean": float(gnn_topk_mean),
+ "physics_topk_mean": float(phys_topk_mean),
+ "gnn_beats_physics_count": n_beat,
+ "gnn_beats_physics_ratio": n_beat / max(len(results), 1),
+ "per_graph": results,
+ }
+
+ return summary
+
+
+# ============================================================================
+# Visualization
+# ============================================================================
+
+
+def visualize_predictions(
+ model: CorrectionGNN,
+ graphs: List[Data],
+ data_dir: Path,
+ out_dir: Path,
+ device: str = "cpu",
+ max_plots: int = 10,
+):
+ """Visualize predicted vs true teacher_mark on mesh."""
+ import matplotlib
+ matplotlib.use("Agg")
+ import matplotlib.pyplot as plt
+ from matplotlib.colors import ListedColormap
+
+ out_dir = Path(out_dir)
+ out_dir.mkdir(parents=True, exist_ok=True)
+
+ model.eval()
+ model.to(device)
+
+ cmap = ListedColormap(["#d0d0d0", "#e74c3c"]) # gray=0, red=1
+
+ plotted = 0
+ for i, g in enumerate(graphs):
+ if plotted >= max_plots:
+ break
+
+ with torch.no_grad():
+ g_device = g.to(device)
+ logits = model(g_device).cpu().numpy().flatten()
+
+ targets = g.y.numpy()
+ physics = g.physics_score_raw.numpy()
+ k = int(targets.sum())
+ if k == 0:
+ continue
+
+ # Predicted top-k
+ pred_mark = np.zeros(len(targets), dtype=int)
+ pred_mark[np.argsort(logits)[-k:]] = 1
+
+ # Physics top-k
+ phys_mark = np.zeros(len(targets), dtype=int)
+ phys_mark[np.argsort(physics)[-k:]] = 1
+
+ # Load raw features to get cell positions (midpoints)
+ d = np.load(data_dir / g.file)
+ features = d["features"] # (n_elem, 15)
+ # features columns 0,1 are midpoint x,y
+ mid_x = features[:, 0]
+ mid_y = features[:, 1]
+
+ fig, axes = plt.subplots(2, 2, figsize=(14, 12))
+ fig.suptitle(f"{g.file} (n={len(targets)}, k={k})", fontsize=12)
+
+ # True teacher_mark
+ ax = axes[0, 0]
+ scatter = ax.scatter(mid_x, mid_y, c=targets, cmap=cmap, s=3, vmin=0, vmax=1)
+ ax.set_title(f"True teacher_mark (k={k})")
+ ax.set_aspect("equal")
+
+ # GNN prediction
+ ax = axes[0, 1]
+ ax.scatter(mid_x, mid_y, c=pred_mark, cmap=cmap, s=3, vmin=0, vmax=1)
+ gnn_overlap = len(set(np.argsort(logits)[-k:]) & set(np.where(targets > 0.5)[0])) / k
+ ax.set_title(f"GNN prediction (topk={gnn_overlap:.3f})")
+ ax.set_aspect("equal")
+
+ # Physics baseline
+ ax = axes[1, 0]
+ ax.scatter(mid_x, mid_y, c=phys_mark, cmap=cmap, s=3, vmin=0, vmax=1)
+ phys_overlap = len(set(np.argsort(physics)[-k:]) & set(np.where(targets > 0.5)[0])) / k
+ ax.set_title(f"Physics baseline (topk={phys_overlap:.3f})")
+ ax.set_aspect("equal")
+
+ # Error map: green=correct, red=wrong
+ ax = axes[1, 1]
+ correct = (pred_mark == targets).astype(int)
+ colors = np.where(correct, "#2ecc71", "#e74c3c")
+ # Highlight true positives and false positives
+ tp = (pred_mark == 1) & (targets == 1)
+ fp = (pred_mark == 1) & (targets == 0)
+ fn = (pred_mark == 0) & (targets == 1)
+ tn = (pred_mark == 0) & (targets == 0)
+
+ ax.scatter(mid_x[tn], mid_y[tn], c="#d0d0d0", s=2, label=f"TN ({tn.sum()})")
+ ax.scatter(mid_x[tp], mid_y[tp], c="#2ecc71", s=8, label=f"TP ({tp.sum()})")
+ ax.scatter(mid_x[fp], mid_y[fp], c="#3498db", s=8, label=f"FP ({fp.sum()})")
+ ax.scatter(mid_x[fn], mid_y[fn], c="#e74c3c", s=8, label=f"FN ({fn.sum()})")
+ ax.legend(fontsize=8, loc="upper right")
+ ax.set_title(f"GNN errors (acc={correct.mean():.3f})")
+ ax.set_aspect("equal")
+
+ fig.tight_layout()
+ fname = out_dir / f"{Path(g.file).stem}_vis.png"
+ fig.savefig(fname, dpi=120)
+ plt.close(fig)
+ plotted += 1
+ print(f" Saved: {fname}")
+
+ if plotted == 0:
+ print(" No plots generated (no positive samples in val set).")
+
+
+# ============================================================================
+# Main
+# ============================================================================
+
+
+def main():
+ parser = argparse.ArgumentParser(description="Test correction GNN")
+ parser.add_argument("--checkpoint", type=str, required=True)
+ parser.add_argument("--data-dir", type=str, required=True)
+ parser.add_argument("--device", type=str, default="cpu")
+ parser.add_argument("--seed", type=int, default=42)
+ parser.add_argument("--val-ratio", type=float, default=0.2)
+ parser.add_argument("--visualize", action="store_true", help="Generate mesh visualizations")
+ parser.add_argument("--max-plots", type=int, default=10)
+ parser.add_argument("--output-dir", type=str, default=str(_PROJECT_ROOT / "outlook" / "result" / "correction"))
+ args = parser.parse_args()
+
+ device = args.device
+ if device == "cuda" and not torch.cuda.is_available():
+ print("CUDA unavailable, falling back to CPU")
+ device = "cpu"
+
+ # Load checkpoint
+ print(f"Loading checkpoint: {args.checkpoint}")
+ ckpt = torch.load(args.checkpoint, map_location=device, weights_only=False)
+ config = ckpt["config"]
+
+ model = CorrectionGNN(
+ node_dim=config["node_dim"],
+ edge_dim=config["edge_dim"],
+ latent_dim=config["latent_dim"],
+ num_mp_steps=config["num_mp_steps"],
+ head_hidden=config["head_hidden"],
+ edge_dropout=0.0,
+ )
+ model.load_state_dict(ckpt["model_state_dict"])
+ model.eval()
+
+ print(f" Epochs trained: {config['epochs']}")
+
+ # Load dataset (same split as training)
+ print("\nLoading dataset...")
+ train_graphs, val_graphs, node_dim, normalizer = load_correction_dataset(
+ data_dir=Path(args.data_dir),
+ val_ratio=args.val_ratio,
+ seed=args.seed,
+ )
+
+ # Store raw physics_score
+ data_dir = Path(args.data_dir)
+ for g in val_graphs:
+ d = np.load(data_dir / g.file)
+ g.physics_score_raw = torch.tensor(d["physics_score"], dtype=torch.float32)
+
+ # Evaluate
+ print("\nEvaluating on validation set...")
+ summary = evaluate(model, val_graphs, device=device)
+
+ print(f"\n{'='*60}")
+ print("Results")
+ print(f"{'='*60}")
+ print(f" Val graphs: {summary['n_graphs']}")
+ print(f" GNN AUC: {summary['gnn_auc']:.4f}")
+ print(f" Physics AUC: {summary['physics_auc']:.4f}")
+ print(f" GNN top-k mean: {summary['gnn_topk_mean']:.4f}")
+ print(f" Physics top-k: {summary['physics_topk_mean']:.4f}")
+ print(f" GNN beats physics: {summary['gnn_beats_physics_count']}/{summary['n_graphs']} "
+ f"({summary['gnn_beats_physics_ratio']*100:.1f}%)")
+
+ # Per-graph detail
+ print(f"\n{'='*60}")
+ print("Per-graph detail:")
+ print(f"{'='*60}")
+ print(f" {'file':30s} {'n':>5s} {'k':>4s} {'gnn':>6s} {'phys':>6s} {'beat':>5s}")
+ print(f" {'-'*30} {'-'*5} {'-'*4} {'-'*6} {'-'*6} {'-'*5}")
+ for r in summary["per_graph"]:
+ beat = "✓" if r["gnn_beats_physics"] else ""
+ print(f" {r['file']:30s} {r['n_cells']:5d} {r['n_positive']:4d} "
+ f"{r['gnn_topk']:6.3f} {r['physics_topk']:6.3f} {beat:>5s}")
+
+ # Save results
+ out_dir = Path(args.output_dir)
+ out_dir.mkdir(parents=True, exist_ok=True)
+ result_path = out_dir / "test_results.json"
+ with open(result_path, "w") as f:
+ json.dump(summary, f, indent=2)
+ print(f"\nResults saved: {result_path}")
+
+ # Visualize
+ if args.visualize:
+ print("\nGenerating visualizations...")
+ visualize_predictions(
+ model, val_graphs, data_dir, out_dir / "vis",
+ device=device, max_plots=args.max_plots,
+ )
+
+ print("\nDone.")
+
+
+if __name__ == "__main__":
+ main()
diff --git a/outlook/src/train.py b/outlook/src/train.py
new file mode 100644
index 0000000..a066a9e
--- /dev/null
+++ b/outlook/src/train.py
@@ -0,0 +1,676 @@
+#!/usr/bin/env python3
+# 训练 budget-conditioned DensityGNN：输入 features_base + budget_code，预测每个初始单元的 density score。
+"""
+run_train_density_gnn_budgeted.py
+==================================
+Train a budget-conditioned DensityGNN on the multi-budget teacher dataset.
+
+Each (sample_id, budget_id) pair becomes one training sample:
+ - Node features: features_base (15-dim) + budget_code (1-dim) = 16-dim
+ budget_code = log(actual_elements[budget_id] / n_init)
+ - Target: log1p(density[budget_id])
+
+Usage:
+ python outlook/src/train.py --data-dir outlook/data --epochs 200
+ python outlook/src/train.py --data-dir outlook/data --epochs 2 --batch-size 2
+"""
+
+import argparse
+import json
+import sys
+import time
+from pathlib import Path
+from typing import Dict, List, Tuple
+
+import numpy as np
+
+_PROJECT_ROOT = Path(__file__).resolve().parent.parent.parent
+sys.path.insert(0, str(_PROJECT_ROOT))
+
+import torch
+import torch.nn as nn
+import torch.optim as optim
+from torch_geometric.data import Data
+from torch_geometric.loader import DataLoader
+
+from outlook.src.feat import append_budget_feature
+from outlook.src.graph import build_graph_from_mesh
+from outlook.src.problem import create_problem_from_params
+from outlook.src.gnn import DensityGNN
+
+OUTLOOK_DIR = _PROJECT_ROOT / "outlook"
+CKPT_DIR = OUTLOOK_DIR / "ckpt"
+CKPT_DIR.mkdir(parents=True, exist_ok=True)
+
+
+# ============================================================================
+# Data loading — expand (sample, budget) pairs into individual graphs
+# ============================================================================
+
+
+def load_budget_dataset(
+ data_dir: Path,
+ budgets_filter: List[int] = None,
+ val_ratio: float = 0.2,
+ seed: int = 42,
+ use_invalid_budgets: bool = False,
+) -> Tuple[List[Data], List[Data], Dict]:
+ """Load multi-budget dataset, expanding each (sample, budget_id) into a graph.
+
+ For each sample .npz:
+ 1. Reconstruct mesh from params → edge_index, edge_attr
+ 2. For each budget_id:
+ - budget_code = log(actual_elements[budget_id] / n_init)
+ - features_16 = append_budget_feature(features_base, actual_elements, n_init)
+ - target = log1p(densities[budget_id])
+ - Build PyG Data
+
+ Parameters
+ ----------
+ data_dir : Path
+ budgets_filter : list of int, optional
+ If set, only use these budget values (must match entries in budgets array).
+ val_ratio : float
+ seed : int
+ use_invalid_budgets : bool
+ If False (default), only use (sample, budget) pairs where valid_budgets=True.
+
+ Returns
+ -------
+ train_graphs, val_graphs, normalizer
+ """
+ data_dir = Path(data_dir)
+ params_data = np.load(data_dir / "params_list.npz")
+ params_array = params_data["params"] # (N, 5)
+ n_samples = len(params_array)
+
+ # Split by sample (not by budget pair) to avoid data leakage
+ rng = np.random.RandomState(seed)
+ indices = np.arange(n_samples)
+ rng.shuffle(indices)
+
+ n_val = max(1, int(n_samples * val_ratio))
+ val_set = set(indices[:n_val].tolist())
+ train_set = set(indices[n_val:].tolist())
+
+ # Collect features for normalization (training only)
+ all_train_features = []
+ train_graphs: List[Data] = []
+ val_graphs: List[Data] = []
+
+ # Track valid/invalid pair counts
+ n_valid_pairs = 0
+ n_invalid_pairs = 0
+ budget_valid_counts: Dict[int, int] = {}
+
+ # Cache mesh reconstruction to avoid rebuilding for same sample
+ mesh_cache: Dict[int, Tuple] = {}
+
+ for sid in range(n_samples):
+ npz_path = data_dir / f"{sid:04d}.npz"
+ if not npz_path.exists():
+ continue
+
+ d = np.load(npz_path)
+ features_base = d["features_base"] # (n_init, 15) float32
+ budgets = d["budgets"] # (B,) int64
+ actual_elements = d["actual_elements"] # (B,) int64
+ densities = d["densities"] # (B, n_init) int32
+ n_init = int(d["n_init"])
+
+ # Load valid_budgets if available (new format), else all True
+ if "valid_budgets" in d:
+ valid_budgets = d["valid_budgets"] # (B,) bool
+ else:
+ valid_budgets = np.ones(len(budgets), dtype=bool)
+
+ params = {
+ "k": float(d["k"]),
+ "eps_r": float(d["eps_r"]),
+ "cx": float(d["cx"]),
+ "cy": float(d["cy"]),
+ "radius": float(d["radius"]),
+ }
+
+ # Reconstruct mesh for graph structure (once per sample)
+ if sid not in mesh_cache:
+ _, initial_mesh = create_problem_from_params(params)
+ template_graph = build_graph_from_mesh(initial_mesh, params, budget_ratio=1.0)
+ mesh_cache[sid] = (template_graph.edge_index, template_graph.edge_attr)
+ edge_index, edge_attr = mesh_cache[sid]
+
+ is_train = sid in train_set
+
+ B = len(budgets)
+ for bi in range(B):
+ # Filter by requested budgets if specified
+ if budgets_filter is not None and int(budgets[bi]) not in budgets_filter:
+ continue
+
+ # Filter by valid_budgets unless --use-invalid-budgets
+ if not use_invalid_budgets and not valid_budgets[bi]:
+ n_invalid_pairs += 1
+ continue
+
+ n_valid_pairs += 1
+ budget_valid_counts.setdefault(int(budgets[bi]), 0)
+ budget_valid_counts[int(budgets[bi])] += 1
+
+ # budget_code uses actual_elements, NOT requested budget
+ target_elements = float(actual_elements[bi])
+ features_16 = append_budget_feature(features_base, target_elements, n_init)
+
+ # Target: log1p(density)
+ density = densities[bi].astype(np.float64)
+ target = np.log1p(density).astype(np.float32)
+
+ x = torch.tensor(features_16, dtype=torch.float32)
+ y = torch.tensor(target, dtype=torch.float32)
+
+ graph = Data(
+ x=x,
+ edge_index=edge_index.clone(),
+ edge_attr=edge_attr.clone(),
+ y=y,
+ )
+ graph.sample_id = sid
+ graph.budget_id = bi
+ graph.requested_budget = int(budgets[bi])
+ graph.actual_elements = int(actual_elements[bi])
+ graph.n_cells = n_init
+ graph.params = params
+
+ if is_train:
+ train_graphs.append(graph)
+ all_train_features.append(features_16)
+ else:
+ val_graphs.append(graph)
+
+ # Compute normalization from training set
+ all_train_features = np.concatenate(all_train_features, axis=0)
+ feat_mean = all_train_features.mean(axis=0).astype(np.float32)
+ feat_std = all_train_features.std(axis=0).astype(np.float32)
+ feat_std[feat_std < 1e-8] = 1.0
+
+ normalizer = {
+ "mean": feat_mean.tolist(),
+ "scale": feat_std.tolist(),
+ }
+
+ mean_t = torch.tensor(feat_mean, dtype=torch.float32)
+ scale_t = torch.tensor(feat_std, dtype=torch.float32)
+
+ for g in train_graphs + val_graphs:
+ g.x = (g.x - mean_t) / scale_t
+
+ print(f" Samples: {n_samples} | Train samples: {len(train_set)} Val samples: {len(val_set)}")
+ print(f" Train pairs: {len(train_graphs)} Val pairs: {len(val_graphs)}")
+ print(f" Valid pairs: {n_valid_pairs} Invalid (skipped): {n_invalid_pairs}")
+ if budget_valid_counts:
+ print(f" Per-budget valid counts:")
+ for b in sorted(budget_valid_counts.keys()):
+ print(f" budget={b:6d} valid={budget_valid_counts[b]}")
+
+ return train_graphs, val_graphs, normalizer
+
+
+# ============================================================================
+# Loss functions
+# ============================================================================
+
+
+def compute_mse_loss(
+ pred: torch.Tensor,
+ target: torch.Tensor,
+ weight: torch.Tensor = None,
+) -> torch.Tensor:
+ """MSE loss, optionally weighted."""
+ if weight is not None:
+ return torch.mean(weight * (pred - target) ** 2)
+ return torch.mean((pred - target) ** 2)
+
+
+def compute_density_weight(
+ target: torch.Tensor,
+ lambda_high: float = 1.0,
+) -> torch.Tensor:
+ """Compute density-based weighting: weight = 1 + lambda_high * normalized(log1p(density)).
+
+ Normalization is per-graph (using batch info) or global min/max.
+ """
+ with torch.no_grad():
+ t_min = target.min()
+ t_max = target.max()
+ if t_max - t_min > 1e-8:
+ t_norm = (target - t_min) / (t_max - t_min)
+ else:
+ t_norm = torch.zeros_like(target)
+ weight = 1.0 + lambda_high * t_norm
+ return weight
+
+
+def compute_monotonic_loss(
+ pred: torch.Tensor,
+ batch_idx: torch.Tensor,
+ actual_elements: torch.Tensor,
+) -> torch.Tensor:
+ """Monotonic loss: for same sample, higher budget → higher score.
+
+ L_mono = mean(ReLU(score_low - score_high))
+ """
+ loss = torch.tensor(0.0, device=pred.device)
+ count = 0
+
+ for sid in batch_idx.unique():
+ mask = batch_idx == sid
+ p = pred[mask]
+ elems = actual_elements[mask]
+
+ # Sort by actual_elements
+ order = torch.argsort(elems)
+ p_sorted = p[order]
+
+ if len(p_sorted) >= 2:
+ diff = p_sorted[:-1] - p_sorted[1:] # low - high
+ loss = loss + torch.relu(diff).sum()
+ count += len(diff)
+
+ return loss / max(count, 1)
+
+
+# ============================================================================
+# Training loop
+# ============================================================================
+
+
+def train(
+ train_graphs: List[Data],
+ val_graphs: List[Data],
+ normalizer: Dict,
+ latent_dim: int = 64,
+ num_mp_steps: int = 3,
+ head_hidden: int = 64,
+ edge_dropout: float = 0.1,
+ batch_size: int = 16,
+ epochs: int = 100,
+ lr: float = 1e-3,
+ weight_decay: float = 1e-4,
+ device: str = "cpu",
+ lambda_high: float = 1.0,
+ use_density_weight: bool = True,
+ mono_weight: float = 0.0,
+) -> Tuple[DensityGNN, List[Dict]]:
+ """Train budget-conditioned DensityGNN."""
+ sample_graph = train_graphs[0]
+ node_dim = sample_graph.x.shape[1]
+ edge_dim = sample_graph.edge_attr.shape[1] if sample_graph.edge_attr.dim() > 1 else 1
+
+ model = DensityGNN(
+ node_dim=node_dim,
+ edge_dim=edge_dim,
+ latent_dim=latent_dim,
+ num_mp_steps=num_mp_steps,
+ head_hidden=head_hidden,
+ edge_dropout=edge_dropout,
+ ).to(device)
+
+ use_gpu = device.startswith("cuda")
+ train_loader = DataLoader(train_graphs, batch_size=batch_size, shuffle=True, pin_memory=use_gpu)
+ val_loader = DataLoader(val_graphs, batch_size=batch_size, shuffle=False, pin_memory=use_gpu)
+
+ optimizer = optim.Adam(model.parameters(), lr=lr, weight_decay=weight_decay)
+ scheduler = optim.lr_scheduler.ReduceLROnPlateau(optimizer, mode="min", factor=0.5, patience=10)
+
+ best_val_loss = float("inf")
+ best_state_dict = None
+ log = []
+
+ for epoch in range(epochs):
+ # -- Train --
+ model.train()
+ train_losses = []
+ for batch in train_loader:
+ batch = batch.to(device)
+ optimizer.zero_grad()
+
+ pred = model(batch)
+ target = batch.y
+
+ if use_density_weight:
+ w = compute_density_weight(target, lambda_high)
+ loss = compute_mse_loss(pred, target, w)
+ else:
+ loss = compute_mse_loss(pred, target)
+
+ if mono_weight > 0 and hasattr(batch, 'actual_elements'):
+ # Build per-node actual_elements tensor
+ actual_elems = torch.zeros(pred.shape[0], device=device)
+ batch_np = batch.batch.cpu().numpy()
+ ae = batch.actual_elements # (num_graphs,) tensor
+ for g_idx in range(batch.num_graphs):
+ g_mask = batch_np == g_idx
+ actual_elems[g_mask] = ae[g_idx]
+ mono_loss = compute_monotonic_loss(pred, batch.batch, actual_elems)
+ loss = loss + mono_weight * mono_loss
+
+ loss.backward()
+ optimizer.step()
+ train_losses.append(loss.item())
+
+ # -- Validate --
+ model.eval()
+ val_losses = []
+ all_preds, all_targets = [], []
+ with torch.no_grad():
+ for batch in val_loader:
+ batch = batch.to(device)
+ pred = model(batch)
+ loss = nn.functional.mse_loss(pred, batch.y)
+ val_losses.append(loss.item())
+ all_preds.append(pred.cpu().numpy())
+ all_targets.append(batch.y.cpu().numpy())
+
+ avg_train = np.mean(train_losses)
+ avg_val = np.mean(val_losses)
+ scheduler.step(avg_val)
+
+ all_preds_cat = np.concatenate(all_preds)
+ all_targets_cat = np.concatenate(all_targets)
+ corr = np.corrcoef(all_preds_cat, all_targets_cat)[0, 1] if len(all_preds_cat) > 1 else 0.0
+
+ # Top-20% overlap
+ top20_overlaps = []
+ model.eval()
+ with torch.no_grad():
+ for batch in val_loader:
+ batch = batch.to(device)
+ pred = model(batch).cpu().numpy()
+ target = batch.y.cpu().numpy()
+ batch_idx = batch.batch.cpu().numpy()
+ for g_id in np.unique(batch_idx):
+ mask = batch_idx == g_id
+ p_g = pred[mask]
+ t_g = target[mask]
+ if len(p_g) < 5:
+ continue
+ n_top = max(1, int(len(p_g) * 0.2))
+ top_pred = set(np.argsort(p_g)[-n_top:])
+ top_true = set(np.argsort(t_g)[-n_top:])
+ top20_overlaps.append(len(top_pred & top_true) / n_top)
+ top20_mean = np.mean(top20_overlaps) if top20_overlaps else 0.0
+
+ entry = {
+ "epoch": epoch,
+ "train_loss": avg_train,
+ "val_loss": avg_val,
+ "val_corr": float(corr),
+ "val_top20_overlap": float(top20_mean),
+ "lr": optimizer.param_groups[0]["lr"],
+ }
+ log.append(entry)
+
+ if epoch % 10 == 0 or epoch == epochs - 1:
+ print(
+ f" Epoch {epoch:3d} | train={avg_train:.4f} val={avg_val:.4f} "
+ f"| corr={corr:.4f} top20={top20_mean:.3f} lr={entry['lr']:.2e}"
+ )
+
+ if avg_val < best_val_loss:
+ best_val_loss = avg_val
+ best_state_dict = {k: v.cpu().clone() for k, v in model.state_dict().items()}
+
+ model.load_state_dict(best_state_dict)
+ return model, log
+
+
+# ============================================================================
+# Per-budget evaluation
+# ============================================================================
+
+
+def evaluate_per_budget(
+ model: DensityGNN,
+ val_graphs: List[Data],
+ normalizer: Dict,
+ device: str = "cpu",
+) -> Dict:
+ """Evaluate model grouped by requested budget."""
+ model.eval()
+ model.to(device)
+
+ budget_groups: Dict[int, List[Data]] = {}
+ for g in val_graphs:
+ b = g.requested_budget
+ budget_groups.setdefault(b, []).append(g)
+
+ results = {}
+ all_preds_combined = []
+ all_targets_combined = []
+
+ for budget in sorted(budget_groups.keys()):
+ graphs = budget_groups[budget]
+ loader = DataLoader(graphs, batch_size=64, shuffle=False)
+
+ preds_list, targets_list = [], []
+ top20_overlaps = []
+
+ with torch.no_grad():
+ for batch in loader:
+ batch = batch.to(device)
+ pred = model(batch).cpu().numpy()
+ target = batch.y.cpu().numpy()
+ preds_list.append(pred)
+ targets_list.append(target)
+
+ batch_idx = batch.batch.cpu().numpy()
+ for g_id in np.unique(batch_idx):
+ mask = batch_idx == g_id
+ p_g = pred[mask]
+ t_g = target[mask]
+ if len(p_g) < 5:
+ continue
+ n_top = max(1, int(len(p_g) * 0.2))
+ top_pred = set(np.argsort(p_g)[-n_top:])
+ top_true = set(np.argsort(t_g)[-n_top:])
+ top20_overlaps.append(len(top_pred & top_true) / n_top)
+
+ preds = np.concatenate(preds_list)
+ targets = np.concatenate(targets_list)
+ mse = float(np.mean((preds - targets) ** 2))
+ corr = float(np.corrcoef(preds, targets)[0, 1]) if len(preds) > 1 else 0.0
+ top20 = float(np.mean(top20_overlaps)) if top20_overlaps else 0.0
+
+ results[f"budget_{budget}"] = {
+ "mse": mse,
+ "corr": corr,
+ "top20_overlap": top20,
+ "n_graphs": len(graphs),
+ }
+
+ all_preds_combined.append(preds)
+ all_targets_combined.append(targets)
+
+ all_preds = np.concatenate(all_preds_combined)
+ all_targets = np.concatenate(all_targets_combined)
+ results["overall"] = {
+ "mse": float(np.mean((all_preds - all_targets) ** 2)),
+ "corr": float(np.corrcoef(all_preds, all_targets)[0, 1]) if len(all_preds) > 1 else 0.0,
+ }
+
+ return results
+
+
+# ============================================================================
+# Main
+# ============================================================================
+
+
+def main():
+ parser = argparse.ArgumentParser(description="Train budget-conditioned DensityGNN")
+ parser.add_argument("--data-dir", type=str, required=True, help="Path to budget dataset directory")
+ parser.add_argument("--epochs", type=int, default=100)
+ parser.add_argument("--batch-size", type=int, default=16)
+ parser.add_argument("--lr", type=float, default=1e-3)
+ parser.add_argument("--weight-decay", type=float, default=1e-4)
+ parser.add_argument("--latent-dim", type=int, default=64)
+ parser.add_argument("--num-mp-steps", type=int, default=3)
+ parser.add_argument("--head-hidden", type=int, default=64)
+ parser.add_argument("--edge-dropout", type=float, default=0.1)
+ parser.add_argument("--device", type=str, default="cpu")
+ parser.add_argument("--checkpoint-out", type=str, default=None,
+ help="Checkpoint path (default: ckpt/budgeted.pt)")
+ parser.add_argument("--budgets", type=str, default=None,
+ help="Comma-separated budgets to train on (default: all)")
+ parser.add_argument("--mono-weight", type=float, default=0.0,
+ help="Weight for monotonic loss (default: 0.0 = disabled)")
+ parser.add_argument("--density-weight", type=float, default=1.0,
+ help="Lambda for density-weighted MSE (default: 1.0, 0 to disable)")
+ parser.add_argument("--seed", type=int, default=42)
+ parser.add_argument("--val-ratio", type=float, default=0.2)
+ parser.add_argument("--use-invalid-budgets", action="store_true",
+ help="Include (sample, budget) pairs where match_ratio is outside valid range")
+ args = parser.parse_args()
+
+ device = args.device
+ if device == "cuda" and not torch.cuda.is_available():
+ print("CUDA unavailable, falling back to CPU")
+ device = "cpu"
+
+ torch.manual_seed(args.seed)
+ np.random.seed(args.seed)
+ if torch.cuda.is_available():
+ torch.cuda.manual_seed_all(args.seed)
+
+ ckpt_path = Path(args.checkpoint_out) if args.checkpoint_out else CKPT_DIR / "budgeted.pt"
+
+ budgets_filter = None
+ if args.budgets:
+ budgets_filter = [int(b) for b in args.budgets.split(",")]
+
+ use_density_weight = args.density_weight > 0
+ lambda_high = args.density_weight if use_density_weight else 0.0
+
+ print("=" * 60)
+ print("Budget-Conditioned DensityGNN Training")
+ print("=" * 60)
+ print(f" Data dir: {args.data_dir}")
+ print(f" Device: {device}")
+ print(f" Epochs: {args.epochs}")
+ print(f" Batch size: {args.batch_size}")
+ print(f" LR: {args.lr}")
+ print(f" Latent dim: {args.latent_dim}")
+ print(f" MP steps: {args.num_mp_steps}")
+ print(f" Density weight: {lambda_high} ({'on' if use_density_weight else 'off'})")
+ print(f" Mono weight: {args.mono_weight}")
+ print(f" Budgets filter: {budgets_filter or 'all'}")
+ print(f" Use invalid: {args.use_invalid_budgets}")
+ print(f" Checkpoint: {ckpt_path}")
+ print()
+
+ # Load data
+ print("Loading budget dataset...")
+ t0 = time.perf_counter()
+ data_dir = Path(args.data_dir)
+ train_graphs, val_graphs, normalizer = load_budget_dataset(
+ data_dir=data_dir,
+ budgets_filter=budgets_filter,
+ val_ratio=args.val_ratio,
+ seed=args.seed,
+ use_invalid_budgets=args.use_invalid_budgets,
+ )
+ print(f" Loaded in {time.perf_counter() - t0:.1f}s")
+
+ # Print budget vs actual_elements summary
+ print("\n Budget mapping (train samples):")
+ budget_actual_map: Dict[int, List[int]] = {}
+ for g in train_graphs:
+ budget_actual_map.setdefault(g.requested_budget, []).append(g.actual_elements)
+ for b in sorted(budget_actual_map.keys()):
+ actuals = budget_actual_map[b]
+ print(f" requested={b:6d} actual: mean={np.mean(actuals):.0f} std={np.std(actuals):.0f} range=[{min(actuals)}, {max(actuals)}]")
+
+ # Train
+ print("\nTraining...")
+ t0 = time.perf_counter()
+ model, log = train(
+ train_graphs, val_graphs, normalizer,
+ latent_dim=args.latent_dim,
+ num_mp_steps=args.num_mp_steps,
+ head_hidden=args.head_hidden,
+ edge_dropout=args.edge_dropout,
+ batch_size=args.batch_size,
+ epochs=args.epochs,
+ lr=args.lr,
+ weight_decay=args.weight_decay,
+ device=device,
+ lambda_high=lambda_high,
+ use_density_weight=use_density_weight,
+ mono_weight=args.mono_weight,
+ )
+ elapsed = time.perf_counter() - t0
+ print(f"\nTraining completed in {elapsed:.1f}s")
+
+ # Save checkpoint
+ torch.save({
+ "model_state_dict": model.state_dict(),
+ "normalizer": normalizer,
+ "training_log": log,
+ "config": {
+ "node_dim": 16,
+ "edge_dim": 1,
+ "latent_dim": args.latent_dim,
+ "num_mp_steps": args.num_mp_steps,
+ "head_hidden": args.head_hidden,
+ "edge_dropout": args.edge_dropout,
+ "epochs": args.epochs,
+ "lr": args.lr,
+ "batch_size": args.batch_size,
+ "weight_decay": args.weight_decay,
+ "density_weight": lambda_high,
+ "mono_weight": args.mono_weight,
+ "seed": args.seed,
+ },
+ }, ckpt_path)
+ print(f"\nCheckpoint saved: {ckpt_path}")
+
+ # Evaluate per budget
+ print("\nEvaluating per budget on validation set...")
+ eval_results = evaluate_per_budget(model, val_graphs, normalizer, device=device)
+
+ print(f"\n{'='*60}")
+ print("Per-budget validation results:")
+ print(f"{'='*60}")
+ for key, val in eval_results.items():
+ if key == "overall":
+ continue
+ print(f" {key:15s} | mse={val['mse']:.4f} corr={val['corr']:.4f} "
+ f"top20={val['top20_overlap']:.3f} (n={val['n_graphs']})")
+ print(f" {'overall':15s} | mse={eval_results['overall']['mse']:.4f} "
+ f"corr={eval_results['overall']['corr']:.4f}")
+
+ # Save eval json
+ eval_path = ckpt_path.with_suffix(".json")
+ eval_output = {
+ "config": {
+ "data_dir": str(args.data_dir),
+ "epochs": args.epochs,
+ "batch_size": args.batch_size,
+ "lr": args.lr,
+ "density_weight": lambda_high,
+ "mono_weight": args.mono_weight,
+ "seed": args.seed,
+ },
+ "per_budget": eval_results,
+ "training_log": log,
+ }
+ with open(eval_path, "w") as f:
+ json.dump(eval_output, f, indent=2)
+ print(f"\nEval results saved: {eval_path}")
+
+ print("\n" + "=" * 60)
+ print("Done.")
+ print("=" * 60)
+
+
+if __name__ == "__main__":
+ main()
diff --git a/outlook/src/train_correction.py b/outlook/src/train_correction.py
new file mode 100644
index 0000000..2e9f3df
--- /dev/null
+++ b/outlook/src/train_correction.py
@@ -0,0 +1,563 @@
+#!/usr/bin/env python3
+"""
+train_correction.py
+===================
+Train a GNN for binary classification of teacher_mark.
+
+Input: concat(features, physics_score[:, None]) → node features (F+1)-dim
+Output: per-cell logit
+Loss: BCEWithLogitsLoss with per-graph pos_weight
+
+Data: outlook/data_correction/sample{XXXX}_step{YYY}.npz
+
+Usage:
+ bash train.sh
+"""
+
+import argparse
+import glob
+import json
+import re
+import sys
+import time
+from pathlib import Path
+from typing import Dict, List, Tuple
+
+import numpy as np
+
+_PROJECT_ROOT = Path(__file__).resolve().parent.parent.parent
+sys.path.insert(0, str(_PROJECT_ROOT))
+
+import torch
+import torch.nn as nn
+import torch.optim as optim
+from torch_geometric.data import Data
+from torch_geometric.loader import DataLoader
+from sklearn.metrics import roc_auc_score
+
+from outlook.src.gnn import DensityGNN
+
+
+# ============================================================================
+# GNN wrapper: change output head to single logit for binary classification
+# ============================================================================
+
+
+class CorrectionGNN(nn.Module):
+ """Reuse DensityGNN backbone, replace density head with binary logit head.
+
+ Also adjusts edge_dim to match computed edge features.
+ """
+
+ def __init__(
+ self,
+ node_dim: int = 16,
+ edge_dim: int = 16,
+ latent_dim: int = 64,
+ num_mp_steps: int = 3,
+ mlp_layers: int = 2,
+ head_hidden: int = 64,
+ activation: str = "leakyrelu",
+ edge_dropout: float = 0.1,
+ ):
+ super().__init__()
+ self.backbone = DensityGNN(
+ node_dim=node_dim,
+ edge_dim=edge_dim,
+ latent_dim=latent_dim,
+ num_mp_steps=num_mp_steps,
+ mlp_layers=mlp_layers,
+ head_hidden=head_hidden,
+ activation=activation,
+ edge_dropout=edge_dropout,
+ )
+ # Replace density regression head → binary logit head
+ self.backbone.head = nn.Sequential(
+ nn.Linear(latent_dim, head_hidden),
+ nn.ReLU(),
+ nn.Linear(head_hidden, 1),
+ )
+
+ def forward(self, graph: Data) -> torch.Tensor:
+ return self.backbone(graph)
+
+
+# ============================================================================
+# Edge feature computation
+# ============================================================================
+
+
+def compute_edge_attr(x: torch.Tensor, edge_index: torch.Tensor) -> torch.Tensor:
+ """Compute edge features as absolute difference of connected node features."""
+ src, dst = edge_index
+ return torch.abs(x[src] - x[dst])
+
+
+# ============================================================================
+# Data loading
+# ============================================================================
+
+
+def load_correction_dataset(
+ data_dir: Path,
+ val_ratio: float = 0.2,
+ seed: int = 42,
+) -> Tuple[List[Data], List[Data], int]:
+ """Load correction dataset, split by sample id.
+
+ Returns
+ -------
+ train_graphs, val_graphs, node_dim
+ """
+ data_dir = Path(data_dir)
+ pattern = str(data_dir / "sample*_step*.npz")
+ all_files = sorted(glob.glob(pattern))
+
+ if not all_files:
+ raise FileNotFoundError(f"No .npz files found matching {pattern}")
+
+ # Parse sample ids
+ sample_files: Dict[int, List[str]] = {}
+ for f in all_files:
+ m = re.search(r"sample(\d+)_step", f)
+ if m:
+ sid = int(m.group(1))
+ sample_files.setdefault(sid, []).append(f)
+
+ sample_ids = sorted(sample_files.keys())
+ print(f" Found {len(all_files)} files across {len(sample_ids)} samples")
+
+ # Split by sample id
+ rng = np.random.RandomState(seed)
+ indices = np.arange(len(sample_ids))
+ rng.shuffle(indices)
+ n_val = max(1, int(len(sample_ids) * val_ratio))
+ val_set = set(sample_ids[i] for i in indices[:n_val])
+ train_set = set(sample_ids[i] for i in indices[n_val:])
+
+ print(f" Train samples: {len(train_set)} Val samples: {len(val_set)}")
+
+ train_graphs: List[Data] = []
+ val_graphs: List[Data] = []
+ node_dim = None
+
+ for sid, files in sample_files.items():
+ is_train = sid in train_set
+ for f in files:
+ d = np.load(f)
+ features = d["features"].astype(np.float32) # (n_elem, F)
+ physics_score = d["physics_score"].astype(np.float32) # (n_elem,)
+ teacher_mark = d["teacher_mark"].astype(np.int64) # (n_elem,)
+ edge_index = torch.tensor(d["edge_index"], dtype=torch.long)
+
+ # x = concat(features, physics_score[:, None])
+ x_np = np.concatenate([features, physics_score[:, None]], axis=1)
+ x = torch.tensor(x_np, dtype=torch.float32)
+
+ if node_dim is None:
+ node_dim = x.shape[1]
+
+ edge_attr = compute_edge_attr(x, edge_index)
+
+ graph = Data(
+ x=x,
+ edge_index=edge_index,
+ edge_attr=edge_attr,
+ y=torch.tensor(teacher_mark, dtype=torch.float32),
+ )
+ graph.sample_id = sid
+ graph.file = Path(f).name
+
+ if is_train:
+ train_graphs.append(graph)
+ else:
+ val_graphs.append(graph)
+
+ # Normalize node features using training stats
+ all_train_x = torch.cat([g.x for g in train_graphs], dim=0)
+ feat_mean = all_train_x.mean(dim=0)
+ feat_std = all_train_x.std(dim=0)
+ feat_std[feat_std < 1e-8] = 1.0
+
+ for g in train_graphs + val_graphs:
+ g.x = (g.x - feat_mean) / feat_std
+ g.edge_attr = compute_edge_attr(g.x, g.edge_index)
+
+ normalizer = {"mean": feat_mean.tolist(), "scale": feat_std.tolist()}
+
+ n_train_graphs = len(train_graphs)
+ n_val_graphs = len(val_graphs)
+ n_train_nodes = sum(g.num_nodes for g in train_graphs)
+ n_val_nodes = sum(g.num_nodes for g in val_graphs)
+ n_train_pos = sum(int(g.y.sum()) for g in train_graphs)
+ n_val_pos = sum(int(g.y.sum()) for g in val_graphs)
+
+ print(f" Train: {n_train_graphs} graphs, {n_train_nodes} nodes, {n_train_pos} positive ({n_train_pos/max(n_train_nodes,1)*100:.1f}%)")
+ print(f" Val: {n_val_graphs} graphs, {n_val_nodes} nodes, {n_val_pos} positive ({n_val_pos/max(n_val_nodes,1)*100:.1f}%)")
+
+ return train_graphs, val_graphs, node_dim, normalizer
+
+
+# ============================================================================
+# Loss with per-graph pos_weight
+# ============================================================================
+
+
+def compute_bce_loss_with_pos_weight(
+ logits: torch.Tensor,
+ targets: torch.Tensor,
+ batch_idx: torch.Tensor,
+) -> torch.Tensor:
+ """BCEWithLogitsLoss with per-graph pos_weight = neg / max(pos, 1).
+
+ Fully vectorized via scatter_add — no Python per-graph loop.
+ """
+ n_graphs = int(batch_idx.max()) + 1
+
+ # Count pos/neg per graph via scatter
+ pos_counts = torch.zeros(n_graphs, device=logits.device)
+ pos_counts.scatter_add_(0, batch_idx.long(), targets)
+ total_counts = torch.zeros(n_graphs, device=logits.device)
+ total_counts.scatter_add_(0, batch_idx.long(), torch.ones_like(targets))
+
+ neg_counts = total_counts - pos_counts
+ pw_per_graph = neg_counts / pos_counts.clamp(min=1.0)
+
+ # Map each node to its graph's pos_weight
+ pw_expanded = pw_per_graph[batch_idx.long()]
+
+ # Weighted BCE: weight = pw for positive, 1 for negative
+ weight = pw_expanded * targets + (1.0 - targets)
+ loss = nn.functional.binary_cross_entropy_with_logits(logits, targets, weight=weight)
+
+ return loss
+
+
+# ============================================================================
+# Metrics
+# ============================================================================
+
+
+def compute_topk_overlap(
+ scores: np.ndarray,
+ targets: np.ndarray,
+ batch_idx: np.ndarray,
+) -> List[float]:
+ """Per-graph top-k overlap: k = number of positive targets."""
+ overlaps = []
+ for g_id in np.unique(batch_idx):
+ mask = batch_idx == g_id
+ s = scores[mask]
+ t = targets[mask]
+ k = int(t.sum())
+ if k == 0 or k >= len(s):
+ continue
+ top_pred = set(np.argsort(s)[-k:])
+ top_true = set(np.where(t > 0.5)[0])
+ overlaps.append(len(top_pred & top_true) / k)
+ return overlaps
+
+
+
+# ============================================================================
+# Training loop
+# ============================================================================
+
+
+def train(
+ train_graphs: List[Data],
+ val_graphs: List[Data],
+ node_dim: int,
+ latent_dim: int = 64,
+ num_mp_steps: int = 3,
+ head_hidden: int = 64,
+ edge_dropout: float = 0.1,
+ batch_size: int = 1,
+ epochs: int = 100,
+ lr: float = 1e-3,
+ weight_decay: float = 1e-4,
+ device: str = "cpu",
+ save_best_path: str = None,
+ normalizer: dict = None,
+) -> Tuple[CorrectionGNN, List[Dict]]:
+ """Train correction GNN."""
+ model = CorrectionGNN(
+ node_dim=node_dim,
+ edge_dim=node_dim, # edge_attr = |x[src] - x[dst]|
+ latent_dim=latent_dim,
+ num_mp_steps=num_mp_steps,
+ head_hidden=head_hidden,
+ edge_dropout=edge_dropout,
+ ).to(device)
+
+ use_gpu = device.startswith("cuda")
+ num_workers = min(4, batch_size) if use_gpu else 0
+ train_loader = DataLoader(train_graphs, batch_size=batch_size, shuffle=True,
+ pin_memory=use_gpu, num_workers=num_workers, persistent_workers=num_workers > 0)
+ val_loader = DataLoader(val_graphs, batch_size=batch_size, shuffle=False,
+ pin_memory=use_gpu, num_workers=num_workers, persistent_workers=num_workers > 0)
+
+ optimizer = optim.Adam(model.parameters(), lr=lr, weight_decay=weight_decay)
+ scheduler = optim.lr_scheduler.ReduceLROnPlateau(optimizer, mode="min", factor=0.5, patience=10)
+ scaler = torch.cuda.amp.GradScaler(enabled=use_gpu)
+
+ best_val_loss = float("inf")
+ best_state_dict = None
+ log = []
+
+ # Pre-compute physics baseline (fixed, no need to recompute every epoch)
+ physics_overlaps = []
+ for g in val_graphs:
+ ps = g.physics_score_raw.numpy() if hasattr(g, 'physics_score_raw') else g.x[:, -1].numpy()
+ t = g.y.numpy()
+ k = int(t.sum())
+ if k == 0 or k >= len(ps):
+ continue
+ top_pred = set(np.argsort(ps)[-k:])
+ top_true = set(np.where(t > 0.5)[0])
+ physics_overlaps.append(len(top_pred & top_true) / k)
+ physics_topk = np.mean(physics_overlaps) if physics_overlaps else 0.0
+
+ t_total = time.perf_counter()
+ for epoch in range(epochs):
+ t_epoch = time.perf_counter()
+
+ # -- Train --
+ model.train()
+ train_losses = []
+ for batch in train_loader:
+ batch = batch.to(device)
+ optimizer.zero_grad()
+
+ with torch.cuda.amp.autocast(enabled=use_gpu):
+ logits = model(batch)
+ targets = batch.y
+ loss = compute_bce_loss_with_pos_weight(logits, targets, batch.batch)
+
+ scaler.scale(loss).backward()
+ scaler.step(optimizer)
+ scaler.update()
+ train_losses.append(loss.item())
+
+ # -- Validate --
+ model.eval()
+ val_losses = []
+ all_logits, all_targets = [], []
+ all_physics_scores = []
+ all_batch_idx = []
+ offset = 0
+
+ with torch.no_grad(), torch.cuda.amp.autocast(enabled=use_gpu):
+ for batch in val_loader:
+ batch = batch.to(device)
+ logits = model(batch)
+ targets = batch.y
+
+ # Per-graph BCE loss
+ loss = compute_bce_loss_with_pos_weight(logits, targets, batch.batch)
+ val_losses.append(loss.item())
+
+ all_logits.append(logits.float().cpu().numpy())
+ all_targets.append(targets.cpu().numpy())
+ all_batch_idx.append(batch.batch.cpu().numpy() + offset)
+ offset += batch.num_graphs
+
+ all_logits_cat = np.concatenate(all_logits)
+ all_targets_cat = np.concatenate(all_targets)
+ all_batch_idx_cat = np.concatenate(all_batch_idx)
+
+ avg_train = np.mean(train_losses)
+ avg_val = np.mean(val_losses)
+ scheduler.step(avg_val)
+
+ # AUC
+ try:
+ auc = roc_auc_score(all_targets_cat, all_logits_cat)
+ except ValueError:
+ auc = 0.0
+
+ # Top-k overlap (model)
+ model_overlaps = compute_topk_overlap(all_logits_cat, all_targets_cat, all_batch_idx_cat)
+ model_topk = np.mean(model_overlaps) if model_overlaps else 0.0
+
+ entry = {
+ "epoch": epoch,
+ "train_loss": float(avg_train),
+ "val_loss": float(avg_val),
+ "val_auc": float(auc),
+ "val_topk_overlap": float(model_topk),
+ "physics_topk_overlap": float(physics_topk),
+ "lr": optimizer.param_groups[0]["lr"],
+ }
+ log.append(entry)
+
+ epoch_time = time.perf_counter() - t_epoch
+
+ if epoch % 10 == 0 or epoch == epochs - 1:
+ total_elapsed = time.perf_counter() - t_total
+ print(
+ f" Epoch {epoch:3d} | train={avg_train:.4f} val={avg_val:.4f} "
+ f"| auc={auc:.4f} topk={model_topk:.3f} phys={physics_topk:.3f} "
+ f"lr={entry['lr']:.2e} | {epoch_time:.1f}s | total={total_elapsed:.1f}s",
+ flush=True,
+ )
+
+ if avg_val < best_val_loss:
+ best_val_loss = avg_val
+ best_state_dict = {k: v.cpu().clone() for k, v in model.state_dict().items()}
+ if save_best_path:
+ torch.save({
+ "model_state_dict": best_state_dict,
+ "normalizer": normalizer,
+ "training_log": log,
+ "config": {
+ "node_dim": node_dim,
+ "edge_dim": node_dim,
+ "latent_dim": latent_dim,
+ "num_mp_steps": num_mp_steps,
+ "head_hidden": head_hidden,
+ "edge_dropout": edge_dropout,
+ "epochs": epochs,
+ "lr": lr,
+ "batch_size": batch_size,
+ },
+ "best_epoch": epoch,
+ "best_val_loss": float(best_val_loss),
+ }, save_best_path)
+
+ model.load_state_dict(best_state_dict)
+ return model, log
+
+
+# ============================================================================
+# Main
+# ============================================================================
+
+
+def main():
+ parser = argparse.ArgumentParser(description="Train teacher_mark binary classifier")
+ parser.add_argument("--data-dir", type=str, required=True)
+ parser.add_argument("--epochs", type=int, default=100)
+ parser.add_argument("--batch-size", type=int, default=1)
+ parser.add_argument("--lr", type=float, default=1e-3)
+ parser.add_argument("--weight-decay", type=float, default=1e-4)
+ parser.add_argument("--latent-dim", type=int, default=64)
+ parser.add_argument("--num-mp-steps", type=int, default=3)
+ parser.add_argument("--head-hidden", type=int, default=64)
+ parser.add_argument("--edge-dropout", type=float, default=0.1)
+ parser.add_argument("--device", type=str, default="cpu")
+ parser.add_argument("--checkpoint-out", type=str, default=None)
+ parser.add_argument("--seed", type=int, default=42)
+ parser.add_argument("--val-ratio", type=float, default=0.2)
+ args = parser.parse_args()
+
+ device = args.device
+ if device == "cuda" and not torch.cuda.is_available():
+ print("CUDA unavailable, falling back to CPU")
+ device = "cpu"
+
+ torch.manual_seed(args.seed)
+ np.random.seed(args.seed)
+ if torch.cuda.is_available():
+ torch.cuda.manual_seed_all(args.seed)
+
+ ckpt_dir = _PROJECT_ROOT / "outlook" / "ckpt"
+ ckpt_dir.mkdir(parents=True, exist_ok=True)
+ ckpt_path = Path(args.checkpoint_out) if args.checkpoint_out else ckpt_dir / "correction.pt"
+ log_path = ckpt_dir / "correction_train_log.json"
+
+ print("=" * 60)
+ print("Teacher-Mark Binary Classifier Training")
+ print("=" * 60)
+ print(f" Data dir: {args.data_dir}")
+ print(f" Device: {device}")
+ print(f" Epochs: {args.epochs}")
+ print(f" Batch size: {args.batch_size}")
+ print(f" LR: {args.lr}")
+ print(f" Latent dim: {args.latent_dim}")
+ print(f" MP steps: {args.num_mp_steps}")
+ print(f" Checkpoint: {ckpt_path}")
+ print(f" Log: {log_path}")
+ print()
+
+ # Load data
+ print("Loading dataset...")
+ t0 = time.perf_counter()
+ train_graphs, val_graphs, node_dim, normalizer = load_correction_dataset(
+ data_dir=Path(args.data_dir),
+ val_ratio=args.val_ratio,
+ seed=args.seed,
+ )
+ print(f" Loaded in {time.perf_counter() - t0:.1f}s")
+
+ # Store raw physics_score in graphs for baseline comparison
+ # Reload to get raw physics_score (before normalization)
+ data_dir = Path(args.data_dir)
+ for g in train_graphs + val_graphs:
+ d = np.load(data_dir / g.file)
+ g.physics_score_raw = torch.tensor(d["physics_score"], dtype=torch.float32)
+
+ # Train
+ print("\nTraining...")
+ t0 = time.perf_counter()
+ best_ckpt_path = ckpt_dir / "correction_best.pt"
+ model, log = train(
+ train_graphs, val_graphs, node_dim,
+ latent_dim=args.latent_dim,
+ num_mp_steps=args.num_mp_steps,
+ head_hidden=args.head_hidden,
+ edge_dropout=args.edge_dropout,
+ batch_size=args.batch_size,
+ epochs=args.epochs,
+ lr=args.lr,
+ weight_decay=args.weight_decay,
+ device=device,
+ save_best_path=str(best_ckpt_path),
+ normalizer=normalizer,
+ )
+ elapsed = time.perf_counter() - t0
+ print(f"\nTraining completed in {elapsed:.1f}s")
+
+ # Save checkpoint
+ torch.save({
+ "model_state_dict": model.state_dict(),
+ "normalizer": normalizer,
+ "training_log": log,
+ "config": {
+ "node_dim": node_dim,
+ "edge_dim": node_dim,
+ "latent_dim": args.latent_dim,
+ "num_mp_steps": args.num_mp_steps,
+ "head_hidden": args.head_hidden,
+ "edge_dropout": args.edge_dropout,
+ "epochs": args.epochs,
+ "lr": args.lr,
+ "batch_size": args.batch_size,
+ "seed": args.seed,
+ },
+ }, ckpt_path)
+ print(f"\nCheckpoint saved: {ckpt_path}")
+
+ # Save training log
+ with open(log_path, "w") as f:
+ json.dump(log, f, indent=2)
+ print(f"Training log saved: {log_path}")
+
+ # Final summary
+ if log:
+ best = min(log, key=lambda e: e["val_loss"])
+ print(f"\n{'='*60}")
+ print(f"Best epoch: {best['epoch']}")
+ print(f" val_loss: {best['val_loss']:.4f}")
+ print(f" val_auc: {best['val_auc']:.4f}")
+ print(f" val_topk: {best['val_topk_overlap']:.3f}")
+ print(f" phys_topk: {best['physics_topk_overlap']:.3f}")
+ beat = best['val_topk_overlap'] > best['physics_topk_overlap']
+ print(f" GNN beats physics: {'YES' if beat else 'NO'}")
+ print(f"{'='*60}")
+
+ print("\nDone.")
+
+
+if __name__ == "__main__":
+ main()
diff --git a/outlook/src/viz_correction.py b/outlook/src/viz_correction.py
new file mode 100644
index 0000000..443182b
--- /dev/null
+++ b/outlook/src/viz_correction.py
@@ -0,0 +1,1074 @@
+#!/usr/bin/env python3
+"""
+viz_correction.py
+=================
+Visualize correction GNN predictions with mesh + field plots.
+
+Two modes:
+ amr — Drive full AMR loop with correction GNN, show final mesh + field + aw_rel
+ step — Per-step comparison: GNN vs teacher vs physics marks on mesh
+
+Usage:
+ # End-to-end AMR
+ python outlook/src/viz_correction.py \
+ --checkpoint outlook/ckpt/correction.pt \
+ --data-dir outlook/data_correction \
+ --mode amr --sample-id 0 --max-elements 5000
+
+ # Per-step comparison
+ python outlook/src/viz_correction.py \
+ --checkpoint outlook/ckpt/correction.pt \
+ --data-dir outlook/data_correction \
+ --mode step --sample-id 0 --step 0
+"""
+
+import argparse
+import copy
+import sys
+from pathlib import Path
+
+import numpy as np
+
+_PROJECT_ROOT = Path(__file__).resolve().parent.parent.parent
+if str(_PROJECT_ROOT) not in sys.path:
+ sys.path.insert(0, str(_PROJECT_ROOT))
+
+import torch
+
+from outlook.src.rollout import run_rollout_to_budget, load_model, _refine_by_eta
+from outlook.src.gen import make_fem_config, build_physics_safe_initial_mesh
+from outlook.src.metrics import compute_mie_error
+
+
+def _interp_error(interp_ref, ref_pts, ref_vals, mesh_target, u_target):
+ """Interpolate a reference solution onto a target mesh and compute error.
+
+ Returns (err_abs, u_ref_at_target) where err_abs = |u_fem - u_ref|.
+ Points outside the convex hull fall back to nearest-neighbor.
+ """
+ from scipy.spatial import cKDTree
+ target_pts = mesh_target.p.T
+ u_ref_at_target = interp_ref(target_pts)
+ nan_mask = np.isnan(u_ref_at_target)
+ if nan_mask.any():
+ tree = cKDTree(ref_pts)
+ _, nn_idx = tree.query(target_pts[nan_mask])
+ u_ref_at_target[nan_mask] = ref_vals[nn_idx]
+ return np.abs(np.real(u_target) - u_ref_at_target), u_ref_at_target
+
+
+
+
+# ============================================================================
+# Mesh reconstruction for a given step (replay AMR from gen.py)
+# ============================================================================
+
+
+def reconstruct_mesh_at_step(params: dict, target_step: int, seed: int = 42):
+ """Replay residual-driven AMR to reconstruct the mesh at a given step.
+
+ Returns (mesh, u_scat) at the target step, or None if step is beyond the AMR history.
+ """
+ from environment.helmholtz import (
+ HelmholtzProblem,
+ _compute_eps_r_at_midpoints,
+ _compute_residual_indicator,
+ )
+ from skfem import Basis, ElementTriP1
+
+ fem_config = make_fem_config(params)
+ problem = HelmholtzProblem(
+ fem_config=fem_config,
+ random_state=np.random.RandomState(seed),
+ )
+ mesh = build_physics_safe_initial_mesh(params)
+
+ mark_fraction = 0.03
+ max_elements = 100000 # won't hit this for replay
+
+ for step in range(target_step + 1):
+ n_elem = mesh.t.shape[1]
+
+ # FEM solve
+ basis = Basis(mesh, ElementTriP1())
+ u_scat = problem.calculate_solution(basis=basis, cache=False)
+
+ if step == target_step:
+ return mesh, u_scat, problem
+
+ # Residual indicator
+ eps_r_arr = _compute_eps_r_at_midpoints(
+ mesh, cx=problem._cx, cy=problem._cy,
+ radius=problem._radius, eps_r_in=problem._eps_r,
+ )
+ eta = _compute_residual_indicator(mesh, u_scat, k=problem._k, eps_r=eps_r_arr)
+
+ # Refine by eta (shared helper)
+ refined = _refine_by_eta(mesh, eta, mark_fraction, max_elements)
+ if refined is None:
+ break
+ mesh = refined
+
+ return mesh, u_scat, problem
+
+
+# ============================================================================
+# Mie reference
+# ============================================================================
+
+
+def compute_mie_on_mesh(mesh, params: dict):
+ """Compute Mie scattered field at mesh vertices."""
+ from environment.mie_solution import mie_scattered_field
+ pts = mesh.p.T
+ return mie_scattered_field(
+ pts, k0=params["k"], eps_r=params["eps_r"],
+ radius=params["radius"], cx=params["cx"], cy=params["cy"],
+ )
+
+
+
+# ============================================================================
+# Visualization: mesh + field (similar to src/visualize.py)
+# ============================================================================
+
+
+# ============================================================================
+# Mesh quality helpers (re-exported from gen.py)
+# ============================================================================
+
+from outlook.src.gen import _mesh_quality_report as check_mesh_valid
+
+
+def render_mesh_field(ax, mesh, scalar, title, show_mesh=True, cmap="jet"):
+ """Render FEM field on mesh using tripcolor."""
+ import matplotlib.tri as tri
+
+ pts = mesh.p.T
+ triang = tri.Triangulation(pts[:, 0], pts[:, 1], mesh.t.T)
+ s = np.abs(scalar) if np.iscomplexobj(scalar) else scalar
+ lmin, lmax = s.min(), s.max()
+ if lmax - lmin < 1e-12:
+ lmin, lmax = lmin - 0.5, lmax + 0.5
+
+ tcf = ax.tripcolor(triang, s, shading="gouraud", cmap=cmap, vmin=lmin, vmax=lmax)
+ if show_mesh:
+ n = triang.triangles.shape[0]
+ ax.triplot(triang, lw=(0.5 if n < 500 else 0.3), color="black",
+ alpha=(0.7 if n < 2000 else 0.5))
+ ax.set_xlim(pts[:, 0].min(), pts[:, 0].max())
+ ax.set_ylim(pts[:, 1].min(), pts[:, 1].max())
+ ax.set_aspect("equal")
+ ax.set_title(title, fontsize=9)
+ ax.set_xticks([])
+ ax.set_yticks([])
+ return tcf
+
+
+def render_marks_on_mesh(ax, mesh, marks, title, label_0="Unmarked", label_1="Marked"):
+ """Render binary marks on mesh cells using colored triangulation."""
+ import matplotlib.tri as tri
+ from matplotlib.colors import ListedColormap
+
+ pts = mesh.p.T
+ triang = tri.Triangulation(pts[:, 0], pts[:, 1], mesh.t.T)
+
+ cmap = ListedColormap(["#d0d0d0", "#e74c3c"])
+ tcf = ax.tripcolor(triang, marks, shading="flat", cmap=cmap, vmin=0, vmax=1)
+ ax.set_xlim(pts[:, 0].min(), pts[:, 0].max())
+ ax.set_ylim(pts[:, 1].min(), pts[:, 1].max())
+ ax.set_aspect("equal")
+ ax.set_title(title, fontsize=9)
+ ax.set_xticks([])
+ ax.set_yticks([])
+ return tcf
+
+
+# ============================================================================
+# Compare plot: Physics vs GNN vs Eta on a given mesh
+# ============================================================================
+
+
+def generate_compare_plot(
+ params: dict,
+ method: str = "neural",
+ mark_fraction: float = 0.03,
+ device: str = "cpu",
+ output_dir: Path = Path("outlook/result/correction/viz"),
+ suffix: str = "compare",
+ ref_elements: int = 20000,
+ max_elements: int = 6000,
+ q: float = 2.0,
+ alpha: float = 0.5,
+ beta: float = 0.5,
+ checkpoint_path: str = None,
+ model=None,
+ normalizer: dict = None,
+):
+ """Generate Physics vs Neural/Hybrid vs Eta comparison.
+
+ All three methods use the SAME run_rollout_to_budget() with budget_mode="strict".
+ """
+ import matplotlib
+ matplotlib.use("Agg")
+ import matplotlib.pyplot as plt
+ from skfem import Basis, ElementTriP1
+
+ output_dir = Path(output_dir)
+ output_dir.mkdir(parents=True, exist_ok=True)
+
+ # ── Run all three to the same target using unified rollout ──
+ result_phys = run_rollout_to_budget(
+ "physics", params, max_elements, q=q,
+ mark_fraction=mark_fraction, device=device, budget_mode="strict",
+ )
+ result_gnn = run_rollout_to_budget(
+ method, params, max_elements, q=q,
+ mark_fraction=mark_fraction, device=device, budget_mode="strict",
+ checkpoint_path=checkpoint_path, model=model, normalizer=normalizer,
+ alpha=alpha, beta=beta,
+ )
+ result_eta = run_rollout_to_budget(
+ "eta", params, max_elements, q=q,
+ mark_fraction=mark_fraction, device=device, budget_mode="strict",
+ )
+
+ mesh_phys, u_phys = result_phys["mesh"], result_phys["u_scat"]
+ mesh_gnn, u_gnn = result_gnn["mesh"], result_gnn["u_scat"]
+ mesh_eta, u_eta = result_eta["mesh"], result_eta["u_scat"]
+
+ method_label = method.capitalize()
+ print(f" [Compare] Physics: {result_phys['actual_elements']} elem "
+ f"aw_rel={result_phys['aw_rel']*100:.2f}%")
+ print(f" [Compare] {method_label:7s}: {result_gnn['actual_elements']} elem "
+ f"aw_rel={result_gnn['aw_rel']*100:.2f}%")
+ print(f" [Compare] Eta: {result_eta['actual_elements']} elem "
+ f"aw_rel={result_eta['aw_rel']*100:.2f}%")
+
+ # ── High-density reference ──
+ from outlook.src.amr import run_residual_teacher
+ from environment.helmholtz import HelmholtzProblem
+
+ fem_config = make_fem_config(params)
+ problem = HelmholtzProblem(
+ fem_config=fem_config,
+ random_state=np.random.RandomState(42),
+ )
+
+ print(f" [Compare] Generating high-density reference ({ref_elements} elem)...")
+ ref_result = run_residual_teacher(
+ problem, initial_mesh=None,
+ max_elements=ref_elements, max_steps=30,
+ refinement_fraction=0.25,
+ )
+ mesh_ref = ref_result["teacher_mesh"]
+ basis_ref = Basis(mesh_ref, ElementTriP1())
+ u_ref = problem.calculate_solution(basis=basis_ref, cache=False)
+ print(f" [Compare] Reference: {mesh_ref.t.shape[1]} elem")
+
+ # ── Interpolate reference onto each refined mesh ──
+ from scipy.interpolate import LinearNDInterpolator
+ ref_pts = mesh_ref.p.T
+ ref_vals = np.real(u_ref)
+ interp_ref = LinearNDInterpolator(ref_pts, ref_vals)
+
+ err_abs_phys, _ = _interp_error(interp_ref, ref_pts, ref_vals, mesh_phys, u_phys)
+ err_abs_gnn, _ = _interp_error(interp_ref, ref_pts, ref_vals, mesh_gnn, u_gnn)
+ err_abs_eta, _ = _interp_error(interp_ref, ref_pts, ref_vals, mesh_eta, u_eta)
+
+ # ── Plot: 2x3 ──
+ cx, cy, radius = params["cx"], params["cy"], params["radius"]
+
+ fig, axes = plt.subplots(2, 3, figsize=(20, 13))
+
+ methods_data = [
+ ("Physics", mesh_phys, u_phys, result_phys, err_abs_phys),
+ (method_label, mesh_gnn, u_gnn, result_gnn, err_abs_gnn),
+ ("Eta", mesh_eta, u_eta, result_eta, err_abs_eta),
+ ]
+
+ # Row 1: FEM field |E_scat|
+ for col, (label, mesh_m, u_m, res_m, _) in enumerate(methods_data):
+ s = np.abs(u_m) if np.iscomplexobj(u_m) else u_m
+ tcf = render_mesh_field(
+ axes[0, col], mesh_m, s,
+ f"{label} |E_scat| ({res_m['actual_elements']} elem)\n"
+ f"aw_rel={res_m['aw_rel']*100:.2f}% max_err={res_m['max_err']:.4f}",
+ show_mesh=True,
+ )
+ axes[0, col].add_patch(plt.Circle((cx, cy), radius, fill=False,
+ edgecolor="cyan", linewidth=1.5, linestyle="--"))
+ fig.colorbar(tcf, ax=axes[0, col], fraction=0.046, pad=0.04)
+
+ # Row 2: |u_fem - u_ref| error map (unified color scale)
+ global_err_max = max(err_abs_phys.max(), err_abs_gnn.max(), err_abs_eta.max())
+ if global_err_max < 1e-12:
+ global_err_max = 1.0
+
+ for col, (label, mesh_m, _, _, err_abs_m) in enumerate(methods_data):
+ tcf2 = render_mesh_field(
+ axes[1, col], mesh_m, err_abs_m,
+ f"{label} |u_fem − u_ref|\n"
+ f"mean={err_abs_m.mean():.4f} max={err_abs_m.max():.4f}",
+ show_mesh=True, cmap="hot",
+ )
+ tcf2.set_clim(0, global_err_max)
+ axes[1, col].add_patch(plt.Circle((cx, cy), radius, fill=False,
+ edgecolor="cyan", linewidth=1.5, linestyle="--"))
+ fig.colorbar(tcf2, ax=axes[1, col], fraction=0.046, pad=0.04)
+
+ k_str = f"k={params['k']:.1f}"
+ method_info = method if method != "hybrid" else f"hybrid(a={alpha},b={beta})"
+ fig.suptitle(
+ f"Field & Error Comparison | {k_str} eps_r={params['eps_r']:.1f} | "
+ f"method={method_info} | target={max_elements} elem -> ref={mesh_ref.t.shape[1]} elem",
+ fontsize=13,
+ )
+ fig.tight_layout()
+ out_path = output_dir / f"{suffix}.png"
+ fig.savefig(out_path, dpi=150, bbox_inches="tight")
+ plt.close(fig)
+ print(f" [Compare] Plot -> {out_path}")
+
+ return out_path
+
+
+def save_ground_truth_plot(
+ params: dict, problem, ref_elements: int = 20000,
+ output_dir: Path = Path("outlook/result/correction/viz"),
+):
+ """Generate and save a standalone high-fidelity reference solution plot.
+
+ Runs residual-driven AMR to `ref_elements`, then plots:
+ - Left: |E_scat| on the refined mesh
+ - Right: Mie |E_scat| on a smooth grid for comparison
+ """
+ import matplotlib
+ matplotlib.use("Agg")
+ import matplotlib.pyplot as plt
+ from skfem import Basis, ElementTriP1
+ from outlook.src.amr import run_residual_teacher
+ from environment.mie_solution import mie_grid_solution
+
+ output_dir = Path(output_dir)
+ output_dir.mkdir(parents=True, exist_ok=True)
+
+ print(f" [GroundTruth] Generating high-fidelity reference ({ref_elements} elem)...")
+ ref_result = run_residual_teacher(
+ problem, initial_mesh=None,
+ max_elements=ref_elements, max_steps=30,
+ refinement_fraction=0.25,
+ )
+ mesh_ref = ref_result["teacher_mesh"]
+ basis_ref = Basis(mesh_ref, ElementTriP1())
+ u_ref = problem.calculate_solution(basis=basis_ref, cache=False)
+
+ err = compute_mie_error(mesh_ref, u_ref, params)
+ print(f" [GroundTruth] Reference: {mesh_ref.t.shape[1]} elem "
+ f"aw_rel={err['aw_rel']*100:.2f}% max_err={err['max_err']:.4f}")
+
+ cx, cy, radius = params["cx"], params["cy"], params["radius"]
+ pts = mesh_ref.p.T
+ xlim = (pts[:, 0].min(), pts[:, 0].max())
+ ylim = (pts[:, 1].min(), pts[:, 1].max())
+
+ mie_grid = mie_grid_solution(
+ params["k"], params["eps_r"], params["radius"],
+ cx, cy, x_range=xlim, y_range=ylim, Nx=500, Ny=500,
+ )
+ mie_grid_abs = np.abs(mie_grid["E_scat"])
+
+ fig, axes = plt.subplots(1, 2, figsize=(14, 6))
+
+ # Left: FEM high-fidelity solution
+ s = np.abs(u_ref) if np.iscomplexobj(u_ref) else u_ref
+ tcf = render_mesh_field(
+ axes[0], mesh_ref, s,
+ f"High-fidelity FEM |E_scat| ({mesh_ref.t.shape[1]} elem)\n"
+ f"aw_rel={err['aw_rel']*100:.2f}% max_err={err['max_err']:.4f}",
+ show_mesh=(mesh_ref.t.shape[1] < 3000),
+ )
+ axes[0].add_patch(plt.Circle((cx, cy), radius, fill=False,
+ edgecolor="cyan", linewidth=1.5, linestyle="--"))
+ fig.colorbar(tcf, ax=axes[0], fraction=0.046, pad=0.04)
+
+ # Right: Mie analytical solution
+ mvmin, mvmax = mie_grid_abs.min(), mie_grid_abs.max()
+ if mvmax - mvmin < 1e-12:
+ mvmin, mvmax = mvmin - 0.5, mvmax + 0.5
+ im = axes[1].pcolormesh(
+ mie_grid["X"], mie_grid["Y"], mie_grid_abs,
+ shading="gouraud", cmap="jet", vmin=mvmin, vmax=mvmax,
+ )
+ axes[1].set_title(f"Mie |E_scat| max={mvmax:.4f}", fontsize=9)
+ axes[1].set_aspect("equal")
+ axes[1].set_xticks([])
+ axes[1].set_yticks([])
+ axes[1].add_patch(plt.Circle((cx, cy), radius, fill=False,
+ edgecolor="cyan", linewidth=1.5, linestyle="--"))
+ fig.colorbar(im, ax=axes[1], fraction=0.046, pad=0.04)
+
+ k_str = f"k={params['k']:.0f}"
+ fig.suptitle(
+ f"Ground Truth Reference | {k_str} eps_r={params['eps_r']:.1f} "
+ f"({cx:.2f},{cy:.2f}) r={radius:.3f}",
+ fontsize=13,
+ )
+ fig.tight_layout()
+ out_path = output_dir / "ground_truth.png"
+ fig.savefig(out_path, dpi=200, bbox_inches="tight")
+ plt.close(fig)
+ print(f" [GroundTruth] Plot → {out_path}")
+ return out_path
+
+
+# ============================================================================
+# Mode: End-to-end AMR
+# ============================================================================
+
+
+def viz_amr(
+ params: dict,
+ method: str = "neural",
+ mark_fraction: float = 0.03,
+ max_elements: int = 5000,
+ max_steps: int = 20,
+ device: str = "cpu",
+ output_dir: Path = Path("outlook/result/correction/viz"),
+ compare: bool = False,
+ alpha: float = 0.5,
+ beta: float = 0.5,
+ q: float = 2.0,
+ checkpoint_path: str = None,
+ model=None,
+ normalizer: dict = None,
+):
+ """Run end-to-end AMR and visualize using unified run_rollout_to_budget()."""
+ import matplotlib
+ matplotlib.use("Agg")
+ import matplotlib.pyplot as plt
+
+ output_dir = Path(output_dir)
+ output_dir.mkdir(parents=True, exist_ok=True)
+
+ # ── Run AMR using unified rollout ──
+ result = run_rollout_to_budget(
+ method, params, max_elements,
+ q=q, mark_fraction=mark_fraction, max_steps=max_steps,
+ checkpoint_path=checkpoint_path, model=model, normalizer=normalizer,
+ device=device, alpha=alpha, beta=beta,
+ budget_mode="strict", save_steps=True, verbose=True,
+ )
+
+ steps_data = result.get("steps", [])
+ mesh = result["mesh"]
+
+ # ── Generate plots ──
+ cx, cy, radius = params["cx"], params["cy"], params["radius"]
+
+ # Overview: all steps in a grid
+ n = len(steps_data)
+ ncols = min(n, 4)
+ nrows = (n + ncols - 1) // ncols
+ fig, axes = plt.subplots(nrows, ncols, figsize=(5 * ncols, 4.5 * nrows))
+ if nrows * ncols == 1:
+ axes = np.array([axes])
+ else:
+ axes = np.array(axes).flatten()
+
+ for i, sd in enumerate(steps_data):
+ tcf = render_mesh_field(
+ axes[i], sd["mesh"], sd["u_scat"],
+ f"Step {i}: {sd['n_elem']} elem, aw_rel={sd['aw_rel']*100:.2f}%",
+ show_mesh=True,
+ )
+ fig.colorbar(tcf, ax=axes[i], fraction=0.046, pad=0.04)
+ axes[i].add_patch(plt.Circle((cx, cy), radius, fill=False,
+ edgecolor="cyan", linewidth=1.5, linestyle="--"))
+
+ for j in range(n, len(axes)):
+ axes[j].set_visible(False)
+
+ fig.subplots_adjust(left=0.04, right=0.92, top=0.90, bottom=0.06, wspace=0.15, hspace=0.30)
+ k_str = f"k={params['k']:.1f}"
+ fig.suptitle(
+ f"Correction GNN AMR | {k_str} eps_r={params['eps_r']:.1f} "
+ f"at ({cx:.2f},{cy:.2f}) r={radius:.3f}",
+ fontsize=12,
+ )
+ overview_path = output_dir / "amr_overview.png"
+ fig.savefig(overview_path, dpi=200, bbox_inches="tight")
+ plt.close(fig)
+ print(f"\n[Viz] Overview -> {overview_path}")
+
+ # Per-step PNGs: FEM field, Mie reference, error map
+ per_step_dir = output_dir / "amr_steps"
+ per_step_dir.mkdir(parents=True, exist_ok=True)
+
+ from environment.mie_solution import mie_grid_solution
+
+ xlim = (mesh.p[0].min(), mesh.p[0].max())
+ ylim = (mesh.p[1].min(), mesh.p[1].max())
+ mie_grid = mie_grid_solution(
+ params["k"], params["eps_r"], params["radius"],
+ params["cx"], params["cy"],
+ x_range=xlim, y_range=ylim, Nx=500, Ny=500,
+ )
+ mie_grid_abs = np.abs(mie_grid["E_scat"])
+
+ for i, sd in enumerate(steps_data):
+ pts = sd["mesh"].p.T
+ u_fem = sd["u_scat"]
+ u_mie = compute_mie_on_mesh(sd["mesh"], params)
+ err_abs = np.abs(u_fem - u_mie)
+
+ ncols_fig = 3
+ fig2, axes2 = plt.subplots(1, ncols_fig, figsize=(6 * ncols_fig, 6))
+ axes2 = list(np.atleast_1d(axes2))
+
+ # Panel 1: FEM field
+ s = np.abs(u_fem) if np.iscomplexobj(u_fem) else u_fem
+ tcf1 = render_mesh_field(
+ axes2[0], sd["mesh"], s,
+ f"Step {i}: FEM |E_scat| ({sd['n_elem']} elem) max={s.max():.4f}",
+ show_mesh=True,
+ )
+ axes2[0].add_patch(plt.Circle((cx, cy), radius, fill=False,
+ edgecolor="cyan", linewidth=1.5, linestyle="--"))
+ fig2.colorbar(tcf1, ax=axes2[0], fraction=0.046, pad=0.04)
+
+ # Panel 2: Mie reference (smooth grid)
+ mvmin, mvmax = mie_grid_abs.min(), mie_grid_abs.max()
+ if mvmax - mvmin < 1e-12:
+ mvmin, mvmax = mvmin - 0.5, mvmax + 0.5
+ im2 = axes2[1].pcolormesh(
+ mie_grid["X"], mie_grid["Y"], mie_grid_abs,
+ shading="gouraud", cmap="jet", vmin=mvmin, vmax=mvmax,
+ )
+ axes2[1].set_title(f"Mie |E_scat| max={mvmax:.4f}", fontsize=9)
+ axes2[1].set_aspect("equal")
+ axes2[1].set_xticks([])
+ axes2[1].set_yticks([])
+ axes2[1].add_patch(plt.Circle((cx, cy), radius, fill=False,
+ edgecolor="cyan", linewidth=1.5, linestyle="--"))
+ fig2.colorbar(im2, ax=axes2[1], fraction=0.046, pad=0.04)
+
+ # Panel 3: Error map
+ evmin, evmax = 0.0, float(err_abs.max()) or 1.0
+ if evmax - evmin < 1e-12:
+ evmax = evmin + 1.0
+ tcf3 = render_mesh_field(
+ axes2[2], sd["mesh"], err_abs,
+ f"|FEM - Mie| aw_rel={sd['aw_rel']*100:.2f}% max={err_abs.max():.4f}",
+ show_mesh=True, cmap="hot",
+ )
+ axes2[2].add_patch(plt.Circle((cx, cy), radius, fill=False,
+ edgecolor="cyan", linewidth=1.5, linestyle="--"))
+ fig2.colorbar(tcf3, ax=axes2[2], fraction=0.046, pad=0.04)
+
+ fig2.tight_layout()
+ fig2.savefig(per_step_dir / f"step{i:02d}.png", dpi=150, bbox_inches="tight")
+ plt.close(fig2)
+
+ print(f"[Viz] Per-step PNGs -> {per_step_dir}/ ({len(steps_data)} files)")
+
+ # ── Compare plot (Physics vs GNN vs Eta) ──
+ if compare:
+ print(f"\n[Compare] Generating Physics vs GNN vs Eta comparison...")
+ generate_compare_plot(
+ params, method=method, mark_fraction=mark_fraction,
+ device=device, output_dir=output_dir, suffix="compare",
+ ref_elements=max_elements * 4, max_elements=max_elements,
+ q=q, alpha=alpha, beta=beta,
+ checkpoint_path=checkpoint_path, model=model, normalizer=normalizer,
+ )
+
+ # ── Save standalone ground truth (high-fidelity reference) ──
+ from environment.helmholtz import HelmholtzProblem
+ fem_config = make_fem_config(params)
+ problem = HelmholtzProblem(
+ fem_config=fem_config,
+ random_state=np.random.RandomState(42),
+ )
+ save_ground_truth_plot(
+ params, problem, ref_elements=max_elements * 4,
+ output_dir=output_dir,
+ )
+
+
+# ============================================================================
+# Mode: Per-step comparison
+# ============================================================================
+
+
+def viz_step(
+ model, normalizer, config, data_dir: Path,
+ sample_id: int = 0, step: int = 0,
+ device: str = "cpu",
+ output_dir: Path = Path("outlook/result/correction/viz"),
+):
+ """Per-step comparison: GNN vs teacher vs physics marks on mesh."""
+ import matplotlib
+ matplotlib.use("Agg")
+ import matplotlib.pyplot as plt
+ from matplotlib.colors import ListedColormap
+
+ output_dir = Path(output_dir)
+ output_dir.mkdir(parents=True, exist_ok=True)
+
+ data_dir = Path(data_dir)
+
+ # Load the sample .npz
+ fname = f"sample{sample_id:04d}_step{step:03d}.npz"
+ fpath = data_dir / fname
+ if not fpath.exists():
+ print(f"Error: {fpath} not found")
+ return
+
+ d = np.load(fpath)
+ params = {
+ "k": float(d["k"]),
+ "eps_r": float(d["eps_r"]),
+ "cx": float(d["cx"]),
+ "cy": float(d["cy"]),
+ "radius": float(d["radius"]),
+ }
+ teacher_mark = d["teacher_mark"]
+ physics_mark = d["physics_mark"]
+ physics_score = d["physics_score"]
+ n_elem = int(d["elements"])
+
+ print(f"[Step] sample={sample_id} step={step} elem={n_elem}")
+ print(f" k={params['k']:.2f} eps_r={params['eps_r']:.2f} "
+ f"cx={params['cx']:.2f} cy={params['cy']:.2f} r={params['radius']:.3f}")
+
+ # Reconstruct mesh at this step
+ print(f" Reconstructing mesh at step {step}...")
+ mesh, u_scat, problem = reconstruct_mesh_at_step(params, target_step=step, seed=42)
+ actual_elem = mesh.t.shape[1]
+ print(f" Reconstructed: {actual_elem} elements")
+
+ # GNN predict
+ from outlook.src.rollout import _predict_gnn
+ probs = _predict_gnn(model, normalizer, mesh, params, device)
+ n_cells = len(probs)
+ n_mark = max(1, int(n_cells * 0.03))
+ if n_mark >= n_cells:
+ pred_mark = np.ones(n_cells, dtype=int)
+ else:
+ pred_mark = np.zeros(n_cells, dtype=int)
+ pred_mark[np.argsort(probs)[-n_mark:]] = 1
+
+ # Compute traditional eta-based marks (same number of cells as GNN)
+ from environment.helmholtz import _compute_eps_r_at_midpoints, _compute_residual_indicator
+ from skfem import Basis, ElementTriP1
+
+ eps_r_arr = _compute_eps_r_at_midpoints(
+ mesh, cx=params["cx"], cy=params["cy"],
+ radius=params["radius"], eps_r_in=params["eps_r"],
+ )
+ eta = _compute_residual_indicator(mesh, u_scat, k=params["k"], eps_r=eps_r_arr)
+
+ n_gnn_selected = int(pred_mark.sum())
+ if n_gnn_selected > 0 and n_gnn_selected < len(eta):
+ eta_mark = np.zeros(len(eta), dtype=int)
+ eta_mark[np.argsort(eta)[-n_gnn_selected:]] = 1
+ else:
+ eta_mark = np.ones(len(eta), dtype=int)
+
+ # Compute overlaps
+ gnn_overlap = 0
+ k = int(teacher_mark.sum())
+ if k > 0 and k < len(teacher_mark):
+ top_gnn = set(np.argsort(probs)[-k:])
+ top_true = set(np.where(teacher_mark > 0.5)[0])
+ gnn_overlap = len(top_gnn & top_true) / k
+
+ phys_overlap = 0
+ if k > 0 and k < len(physics_score):
+ top_phys = set(np.argsort(physics_score)[-k:])
+ top_true = set(np.where(teacher_mark > 0.5)[0])
+ phys_overlap = len(top_phys & top_true) / k
+
+ eta_overlap = 0
+ if k > 0 and k < len(eta):
+ top_eta = set(np.argsort(eta)[-k:])
+ top_true = set(np.where(teacher_mark > 0.5)[0])
+ eta_overlap = len(top_eta & top_true) / k
+
+ # Mie error on current mesh
+ err = compute_mie_error(mesh, u_scat, params)
+
+ print(f" teacher_mark sum: {k}")
+ print(f" GNN top-k overlap: {gnn_overlap:.3f}")
+ print(f" Physics top-k overlap: {phys_overlap:.3f}")
+ print(f" Eta top-k overlap: {eta_overlap:.3f}")
+ print(f" aw_rel (current): {err['aw_rel']*100:.2f}% max_err: {err['max_err']:.4f}")
+
+ # ── Refine using GNN marks ──
+ gnn_selected = np.where(pred_mark == 1)[0]
+ mesh_gnn = mesh.refined(gnn_selected) if len(gnn_selected) > 0 else copy.deepcopy(mesh)
+ basis_gnn = Basis(mesh_gnn, ElementTriP1())
+ u_gnn = problem.calculate_solution(basis=basis_gnn, cache=False)
+ err_gnn = compute_mie_error(mesh_gnn, u_gnn, params)
+
+ # ── Refine using eta marks ──
+ eta_selected = np.where(eta_mark == 1)[0]
+ mesh_eta = mesh.refined(eta_selected) if len(eta_selected) > 0 else copy.deepcopy(mesh)
+ basis_eta = Basis(mesh_eta, ElementTriP1())
+ u_eta = problem.calculate_solution(basis=basis_eta, cache=False)
+ err_eta = compute_mie_error(mesh_eta, u_eta, params)
+
+ # ── Refine using physics marks ──
+ physics_selected = np.where(physics_mark == 1)[0]
+ mesh_phys = mesh.refined(physics_selected) if len(physics_selected) > 0 else copy.deepcopy(mesh)
+ basis_phys = Basis(mesh_phys, ElementTriP1())
+ u_phys = problem.calculate_solution(basis=basis_phys, cache=False)
+ err_phys = compute_mie_error(mesh_phys, u_phys, params)
+
+ print(f" Physics refined: {mesh_phys.t.shape[1]} elem aw_rel={err_phys['aw_rel']*100:.2f}%")
+ print(f" GNN refined: {mesh_gnn.t.shape[1]} elem aw_rel={err_gnn['aw_rel']*100:.2f}%")
+ print(f" Eta refined: {mesh_eta.t.shape[1]} elem aw_rel={err_eta['aw_rel']*100:.2f}%")
+
+ # ── High-density reference solution ──
+ from outlook.src.amr import run_residual_teacher
+ print(f" Generating high-density reference mesh (20000 elem)...")
+ ref_result = run_residual_teacher(
+ problem, initial_mesh=None,
+ max_elements=20000, max_steps=30,
+ refinement_fraction=0.25,
+ )
+ mesh_ref = ref_result["teacher_mesh"]
+ basis_ref = Basis(mesh_ref, ElementTriP1())
+ u_ref = problem.calculate_solution(basis=basis_ref, cache=False)
+ print(f" Reference mesh: {mesh_ref.t.shape[1]} elem, {mesh_ref.p.shape[1]} vertices")
+
+ # Interpolate reference solution onto each refined mesh's vertices
+ from scipy.interpolate import LinearNDInterpolator
+ ref_pts = mesh_ref.p.T # (N_ref, 2)
+ ref_vals = np.real(u_ref)
+ interp_ref = LinearNDInterpolator(ref_pts, ref_vals)
+
+ err_abs_phys, u_ref_phys = _interp_error(interp_ref, ref_pts, ref_vals, mesh_phys, u_phys)
+ err_abs_gnn, u_ref_gnn = _interp_error(interp_ref, ref_pts, ref_vals, mesh_gnn, u_gnn)
+ err_abs_eta, u_ref_eta = _interp_error(interp_ref, ref_pts, ref_vals, mesh_eta, u_eta)
+
+ # ── Plot 1: 2x2 mark comparison ──
+ fig, axes = plt.subplots(2, 2, figsize=(14, 12))
+ cmap = ListedColormap(["#d0d0d0", "#e74c3c"])
+
+ pts = mesh.p.T
+
+ # (0,0) True teacher_mark
+ render_marks_on_mesh(axes[0, 0], mesh, teacher_mark,
+ f"True teacher_mark (k={k})")
+
+ # (0,1) GNN prediction
+ render_marks_on_mesh(axes[0, 1], mesh, pred_mark,
+ f"GNN prediction (topk={gnn_overlap:.3f})")
+
+ # (1,0) Physics baseline
+ render_marks_on_mesh(axes[1, 0], mesh, physics_mark,
+ f"Physics baseline (topk={phys_overlap:.3f})")
+
+ # (1,1) Error map
+ correct = (pred_mark == teacher_mark).astype(int)
+ tp = (pred_mark == 1) & (teacher_mark == 1)
+ fp = (pred_mark == 1) & (teacher_mark == 0)
+ fn = (pred_mark == 0) & (teacher_mark == 1)
+ tn = (pred_mark == 0) & (teacher_mark == 0)
+
+ import matplotlib.tri as tri
+ triang = tri.Triangulation(pts[:, 0], pts[:, 1], mesh.t.T)
+ axes[1, 1].triplot(triang, lw=0.3, color="black", alpha=0.3)
+ axes[1, 1].scatter(pts[mesh.t[:, tn].flatten(), 0], pts[mesh.t[:, tn].flatten(), 1],
+ c="#d0d0d0", s=1, label=f"TN ({tn.sum()})")
+ axes[1, 1].scatter(pts[mesh.t[:, tp].flatten(), 0], pts[mesh.t[:, tp].flatten(), 1],
+ c="#2ecc71", s=8, label=f"TP ({tp.sum()})")
+ axes[1, 1].scatter(pts[mesh.t[:, fp].flatten(), 0], pts[mesh.t[:, fp].flatten(), 1],
+ c="#3498db", s=8, label=f"FP ({fp.sum()})")
+ axes[1, 1].scatter(pts[mesh.t[:, fn].flatten(), 0], pts[mesh.t[:, fn].flatten(), 1],
+ c="#e74c3c", s=8, label=f"FN ({fn.sum()})")
+ axes[1, 1].legend(fontsize=8, loc="upper right")
+ axes[1, 1].set_title(f"GNN errors (acc={correct.mean():.3f})", fontsize=9)
+ axes[1, 1].set_aspect("equal")
+ axes[1, 1].set_xticks([])
+ axes[1, 1].set_yticks([])
+
+ cx, cy, radius = params["cx"], params["cy"], params["radius"]
+ for ax in axes.flatten():
+ ax.add_patch(plt.Circle((cx, cy), radius, fill=False,
+ edgecolor="cyan", linewidth=1.5, linestyle="--"))
+
+ fig.suptitle(
+ f"Correction GNN | sample={sample_id} step={step} | "
+ f"k={params['k']:.1f} eps_r={params['eps_r']:.1f} | "
+ f"{n_elem} elem, aw_rel={err['aw_rel']*100:.2f}%",
+ fontsize=12,
+ )
+ fig.tight_layout()
+ marks_path = output_dir / f"marks_sample{sample_id:04d}_step{step:03d}.png"
+ fig.savefig(marks_path, dpi=150, bbox_inches="tight")
+ plt.close(fig)
+ print(f"\n[Viz] Marks comparison → {marks_path}")
+
+ # ── Plot 2: 2x3 Field + Error comparison (vs high-density reference) ──
+ # Row 1: physics / GNN / eta FEM fields
+ # Row 2: corresponding |u_fem - u_ref| errors
+ fig2, axes2 = plt.subplots(2, 3, figsize=(20, 13))
+
+ methods_data = [
+ ("Physics", mesh_phys, u_phys, err_phys, err_abs_phys),
+ ("GNN", mesh_gnn, u_gnn, err_gnn, err_abs_gnn),
+ ("Eta", mesh_eta, u_eta, err_eta, err_abs_eta),
+ ]
+
+ # Row 1: FEM field |E_scat|
+ for col, (label, mesh_m, u_m, err_m, _) in enumerate(methods_data):
+ s = np.abs(u_m) if np.iscomplexobj(u_m) else u_m
+ tcf = render_mesh_field(
+ axes2[0, col], mesh_m, s,
+ f"{label} |E_scat| ({mesh_m.t.shape[1]} elem)\n"
+ f"aw_rel={err_m['aw_rel']*100:.2f}% max_err={err_m['max_err']:.4f}",
+ show_mesh=True,
+ )
+ axes2[0, col].add_patch(plt.Circle((cx, cy), radius, fill=False,
+ edgecolor="cyan", linewidth=1.5, linestyle="--"))
+ fig2.colorbar(tcf, ax=axes2[0, col], fraction=0.046, pad=0.04)
+
+ # Row 2: |u_fem - u_ref| error map
+ # Use a unified color scale across all three error maps
+ global_err_max = max(err_abs_phys.max(), err_abs_gnn.max(), err_abs_eta.max())
+ if global_err_max <