diff --git a/README.md b/README.md
index f6076a3..82577f1 100644
--- a/README.md
+++ b/README.md
@@ -44,8 +44,8 @@ afem/
 - **入射波**: 沿 -x 方向的平面波 `u_inc = exp(i·k·x)`
 - **散射体**: 圆形介质柱（ε_r 随机采样），位置和半径可配
 - **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=1.5, 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)，^1.5 = 工程折中。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
+- **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
 - **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
 
@@ -54,7 +54,7 @@ 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 + 复数场分解 + 物理参数，节点 12 维 + 边 1 维） |
+| **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 |
@@ -68,10 +68,12 @@ afem/
 ```
 图观测 → MessagePassingBase → MLP → 动作分布 / value 标量
           ├─ nn.Linear（嵌入）
-          ├─ MessagePassingStack（2 层消息传递，inner 残差 + LayerNorm）
-          │    └─ MessagePassingStep × N
-          │         ├─ EdgeModule:  MLP([src | dst | edge_attr])
-          │         └─ NodeModule:  MLP([node | scatter(入边)])
+          ├─ MessagePassingStack（2 层消息传递 + GVN 全局广播，inner 残差 + LayerNorm）
+          │    ├─ MessagePassingStep × N
+          │    │    ├─ 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
 ```
 
@@ -101,31 +103,32 @@ afem/
 
 ## 输入特征
 
-### 节点特征（12 维）
+### 节点特征（13 维）
 
 | 维度 | 来源 | 名称 | 说明 |
 |------|------|------|------|
 | 1 | cfg | `volume` | 无量纲单元面积：volume / λ² |
-| 3 | cfg | `internal_residual` / `gradient_jump` / `sbc_residual` | PDE 残差三分量（无量纲化，经 log₁₀ 压缩）：<br>`(h_K/k_local)·√V·|r|` / `√(½Σ h_e·\|jump\|²/k_local)` / `(h_bnd/k_local)·\|SBC\|` |
+| 3 | cfg | `internal_residual` / `gradient_jump` / `sbc_residual` | PDE 残差三分量（真空波数 k 归一化，经 log₁₀ 压缩）：<br>`(h_K/k)·√V·|r|` / `√(½Σ h_e·\|jump\|²/k)` / `(h_bnd/k)·\|SBC\|` |
 | 1 | cfg | `element_penalty` | 单元惩罚系数 λ |
 | 1 | cfg | `timestep` | 当前 rollout 步数 |
-| 1 | cfg | `wave_number` | Helmholtz 波数 k |
-| 1 | cfg | `k_local_sqrt_vol` | k × √体积（局域波数 × 特征长度） |
+| 1 | cfg | `k_local_sqrt_vol` | k × √(ε_r) × √(V)（局域波数 × 特征长度） |
 | 1 | cfg | `is_sbc_boundary` | 是否与 SBC 吸收边界相邻 (0/1) |
 | 1 | cfg | `dist_to_interface` | 到介质圆柱边界的带符号距离，无量纲化后经 sign·ln(1+|d|) 压缩：`sign(d)·ln(1+|(dist-radius)/λ|)` — 近场近似线性保留分辨力，远场对数压缩避免 OOD，与残差 log₁₀ 风格一致 |
 | 1 | fix | `epsilon_r` | 单元中点相对介电常数（圆柱内 = εᵣ，外 = 1.0） |
-| 1 | fix | `total_solution_magnitude` | 散射场复数解的振幅 |
+| 1 | fix | `total_solution_magnitude` | 散射场振幅 \|u_scat\|（per-element 均值） |
+| 1 | fix | `cos_phase` | Re(u) / (\|u\| + 1e-8)，相位方向余弦，∈ [−1, 1]，无分支切割 |
+| 1 | fix | `sin_phase` | Im(u) / (\|u\| + 1e-8)，相位方向正弦，与 cos 联合编码相位 |
 
 > - **cfg**: 由 `element_features` 配置控制
-> - **fix**: 始终启用（Helmholtz 复数场分解，硬编码）
+> - **fix**: 始终启用（Helmholtz 振幅 + 相位方向，硬编码）
 >
-> GNN 输入用 `_compute_residual_components`（k_local 无量纲化，log₁₀ 压缩）。Reward 用逐单元 η_K（`_eta_indicator`），与 GNN 特征公式一致但不经 log 压缩。
+> GNN 输入用 `_compute_residual_components`（真空波数 k 归一化，log₁₀ 压缩）。Reward 用逐单元 η_K（`_eta_indicator`），与 GNN 特征公式一致但不经 log 压缩。SBC 边界条件保留 `k_local`。
 
 ### 边特征（1 维）
 
 | 维度 | 名称 | 说明 |
 |------|------|------|
-| 1 | `euclidean_distance` | 相邻单元中点欧几里得距离 / λ（无量纲边特征） |
+| 1 | `phase_distance` | 相邻单元中点相位距离 = d × √(k_local_src·k_local_dst) / 2π — 介质内短波长自然放大，赋予 GNN k 不变性 |
 
 
 ---
@@ -144,7 +147,7 @@ main.py --mode train/test/viz
   └─ [train] → ppo.PPOTrainer.fit_iteration() 循环
        ├─ collect_rollouts()           #   256 步 rollout
        │    └─ buffer.compute_returns_and_advantage()
-       │         └─ 单路 GAE          #   逐 agent 时序差分（scatter_add 处理网格细化），奖励含势函数塑形项
+       │         └─ 单路 GAE          #   逐 agent 时序差分（scatter_add 处理网格细化）
        │         └─ Return / value 归一化
        └─ train_step()                 #   多 epoch PPO 更新
             ├─ policy_loss()           #     Clipped PPO
@@ -186,7 +189,7 @@ it | loss ev agents reward x<0 elig sel time
 |------|------|---------|
 | `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 Dörfler-P95 掩码 (η<0.05·η_P95) 滤掉的占比 | 因场景而异，非固定比例 |
+| `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 |
 | `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 |
 
@@ -226,24 +229,25 @@ python src/main.py --mode viz --checkpoint checkpoints/model_final.pt --k-test 3
 
 对 P1 三角单元 K，三项残差分量为：
 
-$$r_{\text{int}} = \frac{h_K}{k_{local}} \sqrt{V_K} \cdot \left| k^2\varepsilon_r u + k^2(\varepsilon_r-1)u_{inc} \right|_K \tag{1}$$
+$$r_{\text{int}} = \frac{h_K}{k} \sqrt{V_K} \cdot \left| k^2\varepsilon_r u + k^2(\varepsilon_r-1)u_{inc} \right|_K \tag{1}$$
 
-$$r_{\text{jump}} = \sqrt{\frac{1}{2}\sum_{e\in\partial K} \frac{h_e}{k_{local}} \cdot \left| [[\nabla u \cdot n]] \right|^2_e} \tag{2}$$
+$$r_{\text{jump}} = \sqrt{\frac{1}{2}\sum_{e\in\partial K} \frac{h_e}{k} \cdot \left| [[\nabla u \cdot n]] \right|^2_e} \tag{2}$$
 
-$$r_{\text{sbc}} = \frac{h_{bnd}}{k_{local}} \cdot \left| \frac{\partial u}{\partial n} - ik_{local}u \right| \tag{3}$$
+$$r_{\text{sbc}} = \frac{h_{bnd}}{k} \cdot \left| \frac{\partial u}{\partial n} - ik_{local}u \right| \tag{3}$$
 
 **逐单元误差指示子**：
 
 $$\eta_K = \sqrt{r_{\text{int}}^2 + r_{\text{jump}}^2 + r_{\text{sbc}}^2}$$
 
-量纲分析（$k_{local} \sim [L]^{-1}$，$h_e \sim [L]$，$|\text{jump}|^2 \sim [L]^{-2}$）：
-三项均严格无量纲：$h_e/k_{local} \cdot |\text{jump}|^2 \sim [L]^2 \cdot [L]^{-2} = 1$。
-细化后 $h_e$ 缩小直接降低跳变项，为 RL agent 提供可感知的正向 reward 信号。
+量纲分析（$k \sim [L]^{-1}$，$h_e \sim [L]$，$|\text{jump}|^2 \sim [L]^{-2}$）：
+三项均严格无量纲：$h_e/k \cdot |\text{jump}|^2 \sim [L]^2 \cdot [L]^{-2} = 1$。
+SBC 边界条件仍用 $k_{local}$（物理正确），仅归一化因子改用 $k$。
+介质内残差不再被 $\sqrt{\varepsilon_r}$ 压低，Agent 获得正确的介质内/外优先级信号。
 
 `η_K` 的计算（`_compute_residual_indicator`）与 GNN 输入特征（`_compute_residual_components`）公式完全一致，特征仅多一层 log₁₀ 压缩。关键验证点：
-- 内部残差：P1 元 ∇²u_h ≡ 0，仅含反应项 `k²ε_r·u + k²(ε_r-1)·u_inc`，除以 `k_local` 后跨介质公平可比
-- 梯度跳变：`(h_e/k_local)·|jump|²`，½ 分配给相邻左右单元；$h_e$ 保留边积分路径，细化后自然衰减
-- SBC 项在 η_K² 中为 `(h_bnd²/k_local²)·|B|²`，分量 `r_sbc = (h_bnd/k_local)·|B|`
+- 内部残差：P1 元 ∇²u_h ≡ 0，仅含反应项 `k²ε_r·u + k²(ε_r-1)·u_inc`，真空波数 k 归一化
+- 梯度跳变：`(h_e/k)·|jump|²`，½ 分配给相邻左右单元；$h_e$ 保留边积分路径，细化后自然衰减
+- SBC 项归一化用 k，物理条件保留 k_local：`(h_bnd²/k²)·|∂u/∂n − i·k_local·u|²`
 
 ### 连续尺寸场策略（score-based + 物理预算约束 + 动作掩码）
 
@@ -258,7 +262,7 @@ N_phys   = ⌈ Σ |K_i| / A_budget_i ⌉       // 全局物理预算（k=30 真
 
 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 ≥ 0.05·η_P95   // 数值底线 + Dörfler-P95
+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)
 num = min(|eligible|, N_current//4, remaining//3)
 selected = top-k by score = -x_i → 1-to-4 切分
 ```
@@ -266,9 +270,9 @@ selected = top-k by score = -x_i → 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 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 1.5），² 为 P1 Helmholtz 理论最优
-- **动作掩码 (Dörfler-P95)**：η_K < 0.05·η_P95 的单元移出候选池。P95 锚定物理误差尺度，免疫远场噪声稀释（与 median/mean 不同），确保只有误差达标的区域消耗细化预算
+- **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
 
 ### 奖励计算
 
@@ -303,10 +307,12 @@ score = -x                                        // x 越小 ⇒ 优先级越
 
 remaining = N_budget − N_old
 max_by_budget = max(0, remaining // 3)
-// 数值底线 + Dörfler-P95 掩码
+// 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_p95 = percentile(η_old, 95)
-eligible = {i | V_old[i] > V_min_safeguard  AND  η_old_i ≥ 0.05·η_p95}
+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
 
@@ -320,42 +326,32 @@ M_new[j] ∈ {0,…,N_old-1}  // 子→父映射
 ||u_h_new||  ← 新解 L₂ 范数
 ```
 
-**Step 3 — 局部奖励**（动态截断 ε_dynamic）
+**Step 3 — 因果奖励**（零和预算审查）
 
-ε_dynamic = max(0.01 × η_P95, 1e-6)           // P95 锚定，免疫远场噪声稀释
-ε_dynamic = max(0.05 × mean(η_new), 1e-6)        // 自适应钳制，切断远场低 η 区 reward hacking
-spatial:      r_local_i = log(η_old_i + ε_dynamic) − log( √(Σ_{j: M_new[j]=i} η_new_j²) + ε_dynamic )
-spatial_max:  r_local_i = log(η_old_i + ε_dynamic) − log( max_{j: M_new[j]=i} η_new_j + ε_dynamic )
-```
+ε_dynamic = max(0.01 × η_P95, 1e-6)
 
-> **L₂ 聚合保证 r_local ≥ 0**: 对 1-to-4 切分：
-> ```
-> Σ η_child² = int²/4 + jump² + sbc²   ≤   η_parent² = int² + jump² + sbc²
-> → r_local = ½[log(η_parent²) − log(Σ η_child²)] ≥ 0
-> ```
-> - 纯 int 主导: r_local = log(2) ≈ 0.69（强正奖励）
-> - 纯 jump/sbc 主导: r_local = 0（中性，不惩罚不奖励）
-> - **永远不会惩罚细化**——与 L₁ sum 不同，L₂ 天然避免了对 jump/sbc 主导区的结构性负偏置。
+// 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
 
-**Step 4 — 动作惩罚**
+// Unrefined parents: causal isolation
+else:
+    r_i = 0
 
-```
-penalty_i = λ · (n_i − 1)                                              // λ = 0.06
-          + (λ_limit / N_old) · 𝟙[达到最大单元数上限]                    // λ_limit = 10000
+> **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。
 
-r_local_i ← r_local_i − penalty_i
-```
+**Step 4 — 全局误差（仅诊断）**
 
-**Step 5 — 全局势函数塑形**（仅发给被细化的父单元）
+global_bonus = α·[log(E_old) − log(E_new)]，α = 0.5
 
-```
-E_global = √(Σ_K η_K²) / ||u_h||_{L₂(Ω)}
-global_bonus = α · [ log(E_global_old) − log(E_global_new) ]           // α = 0.2
-
-r_i = r_local_i − penalty_i  +  global_bonus · 𝟙[i 被细化]              // 未细化的单元 reward ≈ 0
-```
-
-> 全局改进信号只分配给实际参与细化的单元，避免被未细化单元稀释。
+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。
 
 ---
 
@@ -378,19 +374,21 @@ r_i = r_local_i − penalty_i  +  global_bonus · 𝟙[i 被细化]
 
 | 组件 | 聚合 | 作用 |
 |------|------|------|
-| 局部项 `log(η_old / √(Σ η_child²))` | scatter_add（子→父求平方和再开方） | L₂ 聚合保证 r_local ≥ 0：不惩罚任何细化，int 主导区获强正奖励 (≈+0.69)，纯 jump/sbc 区中性 |
-| 动作惩罚 `λ(n_i−1)` λ=0.02 | per-parent | 轻微抑制网格膨胀（1-to-4 切分扣 0.06，仅占 r_local 的 ~16%） |
-| 元素上限惩罚 | 达到 20000 上限时触发 | 极端情况兜底，λ_limit / N_old ≈ 0.05~0.5 per agent |
-| 全局项 `α·ΔlogE` α=0.2 | 仅细化父单元 | L₂ 无量纲全局误差下降趋势，只发给实际参与细化的单元，避免被未细化单元稀释 |
+| 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 |
 
 ---
 
 ## PPO 关键细节
 
-- **单路 GAE**: 势函数塑形后的奖励已包含全局改进信号，用 `scatter_add` 将细化后的子单元值聚合回父单元，单路 GAE 即可
+- **单路 GAE**: r_local 自身已闭合因果（细化单元的局部误差改善），不需要势函数塑形。用 `scatter_add` 将细化后的子单元值聚合回父单元，单路 GAE 即可
 - **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 `[-4.0, -1.0]`，std ∈ [0.018, 0.368]<br>
-  初始化 `-2.0` (std≈0.135)，避免 `continuous_sizing_field` 有效范围 [-3, 3] 内噪声过大
-- **熵正则**: `entropy_coefficient=0.001`，防止 log_std 过早收敛
+- **log_std clamp**: 每步 `optimizer.step()` 后将 `log_std` clamp 到 `[-3.0, -1.0]`，σ ∈ [0.05, 0.37]<br>
+  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
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diff --git a/environment/fem_problem.py b/environment/fem_problem.py
index a3f781e..d3392f1 100644
--- a/environment/fem_problem.py
+++ b/environment/fem_problem.py
@@ -142,6 +142,10 @@ class FEMProblemWrapper:
     def plot_boundary(self):
         return self._plot_boundary
 
+    @property
+    def last_solve_timing(self) -> Optional[Dict[str, float]]:
+        return getattr(self.fem_problem, "_last_solve_timing", None)
+
     # ---- 额外的 plotly 渲染图层 ----
     def additional_plots(self) -> Dict:
         return self.fem_problem.additional_plots_from_mesh(self._mesh)
diff --git a/environment/helmholtz.py b/environment/helmholtz.py
index 1a2eeb5..9fa85ea 100644
--- a/environment/helmholtz.py
+++ b/environment/helmholtz.py
@@ -1,4 +1,5 @@
 import copy
+import time
 from typing import Any, Dict, List, Optional, Union
 
 import numpy as np
@@ -71,7 +72,7 @@ class HelmholtzProblem:
         boundary = domain_cfg.get("boundary", [0, 0, 1, 1])
         domain_area = (boundary[2] - boundary[0]) * (boundary[3] - boundary[1])
         k_ref = helmholtz_config.get("k_ref", 6.0)
-        k_exponent = helmholtz_config.get("k_exponent", 1.5)
+        k_exponent = helmholtz_config.get("k_exponent", 2.0)
         base_elements = domain_cfg.get("initial_num_elements", 400)
         scaled_elements = int(base_elements * (self._k / k_ref) ** k_exponent * domain_area)
         domain_cfg["initial_num_elements"] = max(scaled_elements, int(base_elements * domain_area))
@@ -104,8 +105,13 @@ class HelmholtzProblem:
         return Basis(mesh, ElementTriP1())
 
     def calculate_solution(self, basis: Basis, cache: bool = False) -> np.ndarray:
+        _t = {}
+
+        _t0 = time.perf_counter()
         K = asm(self._bilin_form, basis)
+        _t1 = time.perf_counter()
         f = asm(self._lin_form_real, basis) + 1j * asm(self._lin_form_imag, basis)
+        _t2 = time.perf_counter()
 
         boundary_facets = basis.mesh.boundary_facets()
         facet_basis = FacetBasis(basis.mesh, basis.elem, facets=boundary_facets)
@@ -115,8 +121,18 @@ class HelmholtzProblem:
             return u * v
 
         M_boundary = asm(boundary_mass, facet_basis)
+        _t3 = time.perf_counter()
         K_total = K.astype(np.complex128) - 1j * self._k * M_boundary
         u_scat = solve(K_total, f)
+        _t4 = time.perf_counter()
+
+        _t["assemble_K"]     = _t1 - _t0
+        _t["assemble_f"]     = _t2 - _t1
+        _t["assemble_boundary"] = _t3 - _t2
+        _t["solve"]          = _t4 - _t3
+        _t["total"]          = _t4 - _t0
+        _t["n_dof"]          = int(basis.mesh.p.shape[1])
+        self._last_solve_timing = _t
 
         return u_scat
 
@@ -262,20 +278,20 @@ def _compute_residual_indicator(
     """
     基于残差的逐单元后验误差估计 — 无量纲化版本。
 
-    引入局部波数 k_local = k√ε_r 消除纯几何尺度 h 带来的特征偏差，
-    使误差指示子反映"相位分辨率残差"而非"网格粗疏程度"。
+    使用真空波数 k₀ 归一化（非 k_local），使误差指示子反映"绝对物理误差"
+    而非"相对局部波长的分辨率"。介质内短波（ε_r>1）的残差在 k_local 下被
+    压低 √ε_r 倍，改用 k₀ 后介质内 η 自然放大，Agent 获得正确优先级。
 
     P1 单元三项:
-        1. r_int  = (h_K/k_local)·√V_K · |k²ε_r·u_h + k²(ε_r-1)·u_inc|
-        2. r_jump = √(½ Σ_{e∈∂K} (h_e/k_local)·|[[∇u_h·n]]|²)
-        3. r_sbc  = (h_bnd/k_local)·|∂u/∂n - i·k_local·u|
+        1. r_int  = (h_K/k)·√V_K · |k²ε_r·u_h + k²(ε_r-1)·u_inc|
+        2. r_jump = √(½ Σ_{e∈∂K} (h_e/k)·|[[∇u_h·n]]|²)
+        3. r_sbc  = (h_bnd/k)·|∂u/∂n - i·k_local·u|   (SBC 条件仍用 k_local)
 
     Returns:
         eta_elements: shape (num_elements,) 的逐单元误差指标
     """
     n_elements = mesh.t.shape[1]
     eps_r = np.asarray(eps_r)
-    k_local = k * np.sqrt(np.maximum(eps_r, 1.0))
 
     # ── 1. 单元几何量 ──
     i0, i1, i2 = mesh.t[0], mesh.t[1], mesh.t[2]
@@ -307,7 +323,7 @@ def _compute_residual_indicator(
     f_mid = (k**2) * (eps_r - 1.0) * u_inc_mid
     r_mid = f_mid + (k**2) * eps_r * u_mid
 
-    cell_residual_sq = (h_K**2) * element_areas * np.abs(r_mid) ** 2 / (k_local ** 2)
+    cell_residual_sq = (h_K**2) * element_areas * np.abs(r_mid) ** 2 / (k ** 2)
     cell_residual_sq[element_areas < 1e-15] = 0.0
 
     # ── 4. 内部边梯度跳变 ──
@@ -327,8 +343,8 @@ def _compute_residual_indicator(
     jump_val_sq = jump_val ** 2
 
     jump_residual_sq = np.zeros(n_elements)
-    np.add.at(jump_residual_sq, elem_left, 0.5 * h_e * jump_val_sq / k_local[elem_left])
-    np.add.at(jump_residual_sq, elem_right, 0.5 * h_e * jump_val_sq / k_local[elem_right])
+    np.add.at(jump_residual_sq, elem_left, 0.5 * h_e * jump_val_sq / k)
+    np.add.at(jump_residual_sq, elem_right, 0.5 * h_e * jump_val_sq / k)
 
     # ── 5. 合并 ──
     eta_sq = cell_residual_sq + jump_residual_sq
@@ -356,7 +372,7 @@ def _compute_residual_indicator(
             + u_h[mesh.facets[1, boundary_facets_idx]]
         ) / 2.0
         sbc_residual = du_dn - 1j * k_local * u_edge_mean
-        sbc_residual_sq = (h_bnd ** 2) * np.abs(sbc_residual) ** 2 / (k_local ** 2)
+        sbc_residual_sq = (h_bnd ** 2) * np.abs(sbc_residual) ** 2 / (k ** 2)
         np.add.at(eta_sq, bnd_elem, sbc_residual_sq)
 
     eta_sq = np.maximum(eta_sq, 0.0)
@@ -373,13 +389,13 @@ def _compute_residual_components(
     """
     计算逐单元的三项 PDE 物理残差（分离版，无量纲化）。
 
-    引入 k_local = k√ε_r 消除几何尺度偏差，使 GNN 跨介质公平感知"相位分辨率残差"。
-    保留源项信息（k²(ε_r-1)·u_inc），确保极粗网格下介质内部巨大物理激励仍可被网络捕捉。
+    使用真空波数 k₀ 归一化 — 介质内短波残差不再被 k_local 压低，GNN 获得
+    正确的介质内/外优先级信号。
 
     P1 单元返回:
-        internal_residual: (h_K/k_local)·√V_i · |k²ε_r·u + k²(ε_r-1)·u_inc|
-        gradient_jump:     √(½ Σ_{e∈∂K_i} (h_e/k_local)·|[[∇u·n]]|²)
-        sbc_residual:      (h_bnd/k_local)·|∂u/∂n - i·k_local·u|
+        internal_residual: (h_K/k)·√V_i · |k²ε_r·u + k²(ε_r-1)·u_inc|
+        gradient_jump:     √(½ Σ_{e∈∂K_i} (h_e/k)·|[[∇u·n]]|²)
+        sbc_residual:      (h_bnd/k)·|∂u/∂n - i·k_local·u|   (SBC 条件仍用 k_local)
         element_areas:     单元面积
         is_sbc_boundary:   该单元是否与 SBC 边界相邻 (0/1)
 
@@ -388,7 +404,6 @@ def _compute_residual_components(
     """
     n_elements = mesh.t.shape[1]
     eps_r = np.asarray(eps_r)
-    k_local = k * np.sqrt(np.maximum(eps_r, 1.0))
 
     # ── 1. 单元几何量 ──
     i0, i1, i2 = mesh.t[0], mesh.t[1], mesh.t[2]
@@ -421,7 +436,7 @@ def _compute_residual_components(
     u_inc_mid = np.exp(1j * k * x_mid)
     f_mid = (k**2) * (eps_r - 1.0) * u_inc_mid
     r_mid = f_mid + (k**2) * eps_r * u_mid
-    internal_residual = (h_K / k_local) * np.sqrt(element_areas) * np.abs(r_mid)
+    internal_residual = (h_K / k) * np.sqrt(element_areas) * np.abs(r_mid)
     internal_residual[element_areas < 1e-15] = 0.0
 
     # ── 4. 内部边梯度跳变 (逐单元) ──
@@ -441,8 +456,8 @@ def _compute_residual_components(
 
     gradient_jump = np.zeros(n_elements, dtype=np.float64)
     jump_sq_per_edge = jump_val ** 2
-    np.add.at(gradient_jump, elem_left, 0.5 * h_e * jump_sq_per_edge / k_local[elem_left])
-    np.add.at(gradient_jump, elem_right, 0.5 * h_e * jump_sq_per_edge / k_local[elem_right])
+    np.add.at(gradient_jump, elem_left, 0.5 * h_e * jump_sq_per_edge / k)
+    np.add.at(gradient_jump, elem_right, 0.5 * h_e * jump_sq_per_edge / k)
     gradient_jump = np.sqrt(gradient_jump)
 
     # ── 5. SBC 边界残差 + 边界标记 ──
@@ -470,7 +485,7 @@ def _compute_residual_components(
             + u_h[mesh.facets[1, boundary_facets_idx]]
         ) / 2.0
         sbc_val = np.abs(du_dn - 1j * k_local * u_edge_mean)
-        np.add.at(sbc_residual, bnd_elem, (h_bnd / k_local) * sbc_val)
+        np.add.at(sbc_residual, bnd_elem, (h_bnd / k) * sbc_val)
         is_sbc_boundary[bnd_elem] = 1.0
 
     # ── 对数预处理：压缩跨数量级动态范围（仅 GNN 特征需要）──
diff --git a/environment/mesh_refinement.py b/environment/mesh_refinement.py
index 2947b33..88fe0b1 100644
--- a/environment/mesh_refinement.py
+++ b/environment/mesh_refinement.py
@@ -166,8 +166,11 @@ class MeshRefinement(gym.Env):
             feats["dist_to_interface"] = lambda: self._dist_to_interface
 
         # Complex field decomposition (always present for Helmholtz)
+        # amplitude + phase direction (cos/sin ∈ [−1,1]), ε=1e-8 at |u|→0 nodes
         feats["epsilon_r"] = lambda: self._epsilon_r_elements
         feats["total_solution_magnitude"] = lambda: np.abs(self._complex_solution_mean)
+        feats["cos_phase"] = lambda: np.real(self._complex_solution_mean) / (np.abs(self._complex_solution_mean) + 1e-8)
+        feats["sin_phase"] = lambda: np.imag(self._complex_solution_mean) / (np.abs(self._complex_solution_mean) + 1e-8)
         return feats
 
     def reset(self) -> Data:
@@ -218,6 +221,8 @@ class MeshRefinement(gym.Env):
         self._reward = 0
         self._cumulative_return = 0
         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
 
         # reset internal state that tracks statistics over the episode
         self._previous_error_per_element = self.error_per_element
@@ -344,6 +349,8 @@ class MeshRefinement(gym.Env):
                     "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,
                 }
             )
@@ -528,8 +535,9 @@ class MeshRefinement(gym.Env):
             #  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
             #
-            #  动作掩码 (Dörfler-P95): η_K < 0.05·η_P95 的单元移出候选池，
-            #   P95 锚定物理误差尺度，免疫远场噪声稀释，强制预算投入误差主导区
+            #  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
             # ================================================================
             x = action.flatten()
 
@@ -542,6 +550,8 @@ class MeshRefinement(gym.Env):
             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
                 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）
@@ -559,13 +569,31 @@ class MeshRefinement(gym.Env):
             # Filter 1: numerical safeguard only — no physics heuristic
             area_eligible = np.where(self.element_volumes > V_min_safeguard)[0]
 
-            # Filter 2: Dörfler-style action mask — exclude elements below 5% of η_P95
-            # P95 anchors the threshold to physically meaningful error scale,
-            # immune to far-field noise dilution (unlike median or mean).
-            # η_K < 0.05·η_P95 → not worth the refinement budget.
+            # 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.
             eta_current = self._eta_indicator
-            eta_p95 = np.percentile(eta_current, 95)
-            error_eligible = np.where(eta_current >= 0.05 * eta_p95)[0]
+            eta_sq = eta_current ** 2
+            total_energy = np.sum(eta_sq)
+
+            if total_energy > 0:
+                idx_asc = np.argsort(eta_current)  # ascending
+                cumsum_asc = np.cumsum(eta_sq[idx_asc])
+                eps_noise = 0.01  # bottom 1% of energy = noise tail
+                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
+                error_eligible = idx_asc[k:]
+            else:
+                self._diag_dorfler_tail_ratio = 0.0
+                self._diag_dorfler_floor_active = False
+                error_eligible = np.arange(self._num_elements)
 
             eligible = np.intersect1d(area_eligible, error_eligible)
 
@@ -687,6 +715,7 @@ class MeshRefinement(gym.Env):
         graph_dict = graph_dict | self._get_graph_edges()
 
         observation_graph = Data(**graph_dict)
+        observation_graph.eta = torch.tensor(self._eta_indicator, dtype=torch.float32)
 
         return observation_graph
 
@@ -755,8 +784,16 @@ class MeshRefinement(gym.Env):
                 - self._element_midpoints[src_nodes],
                 axis=1,
             )
-            lam = 2.0 * np.pi / self._wave_number
-            edge_features[:, edge_feature_position] = euclidean_distances / lam
+            # Phase distance: physical edge length in local wavelengths.
+            # k_local = k·√ε_r adapts to the medium — two elements are "farther
+            # apart" in phase inside high-ε regions where the wave oscillates
+            # faster.  This gives the GNN a k-invariant metric for generalisation.
+            k_local_src = self._wave_number * np.sqrt(np.maximum(
+                self._epsilon_r_elements[src_nodes], 1.0))
+            k_local_dst = self._wave_number * np.sqrt(np.maximum(
+                self._epsilon_r_elements[dest_nodes], 1.0))
+            k_edge = np.sqrt(k_local_src * k_local_dst)  # geometric mean
+            edge_features[:, edge_feature_position] = euclidean_distances * k_edge / (2.0 * np.pi)
             edge_feature_position += 1
         edge_index = torch.tensor(np.vstack((src_nodes, dest_nodes))).long()
         edge_attr = torch.tensor(edge_features, dtype=torch.float32)
@@ -895,8 +932,30 @@ class MeshRefinement(gym.Env):
 
         reward_per_agent = self.project_to_scalar(reward_per_agent_and_dim)
 
-        # apply action/element penalty
+        # ── 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).
         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
+        )
+
+        # Unrefined: clean zero (causal isolation)
+        reward_per_agent[~refined_mask] = 0.0
+
+        # 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)
         element_limit_penalty = (
@@ -908,7 +967,12 @@ class MeshRefinement(gym.Env):
             reward_per_agent - element_penalty - element_limit_penalty
         )
 
-        # ── Potential-based shaping: only refined parents get the global bonus ──
+        # ── 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)))
@@ -917,8 +981,7 @@ class MeshRefinement(gym.Env):
         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))
-        refined_parents = unique_old[counts > 1]
-        reward_per_agent[refined_parents] += global_bonus
+        # global_bonus intentionally NOT added to reward_per_agent — see above.
 
         self._reward_per_agent = reward_per_agent
         self._cumulative_reward_per_agent = (
@@ -1087,7 +1150,7 @@ class MeshRefinement(gym.Env):
     @property
     def is_terminal(self) -> bool:
         # Agent selected nothing to refine — budget exhausted or
-        # Doerfler mask filtered everything.  Episode converged naturally.
+        # Reverse Dörfler mask filtered everything.  Episode converged naturally.
         # -1 = not yet evaluated (reset state), 0 = nothing selected this step.
         sc = getattr(self, "_diag_selected_count", -1)
         if sc == 0:
diff --git a/git.txt b/git.txt
new file mode 100644
index 0000000..5fd114b
--- /dev/null
+++ b/git.txt
@@ -0,0 +1,8 @@
+linux服务器：scp -r dxw@222.20.97.222:/public/home/dxw/Codes/afem/*  ./
+本机：git init
+	git branch -M main
+	git add .
+	git commit -m "first commit"
+	git remote set-url origin http://duxiaowei@222.20.97.33:3000/duxiaowei/afem.git
+	git remote -v（仅确认状态使用）
+	git push -u origin main
\ No newline at end of file
diff --git a/logs/before.out b/logs/before.out
new file mode 100644
index 0000000..81692b3
--- /dev/null
+++ b/logs/before.out
@@ -0,0 +1,418 @@
+Starting training at Thu 28 May 13:25:52 CST 2026
+Running on node: node06
+[Device] cuda
+[Env] node_feats=12 edge_feats=1 act_dim=1
+[Model] params=76,099
+     1/401 | loss=0.8482 ev=0.001 agents=84 avg_r=-1.5801 sum_r=-404.50 x<0=0.09 elig=0.59 dorfler_tail=0.08 floor=0 sel=35 n_ref=0 r_loc=0.000 8.5s
+     2/401 | loss=1.0257 ev=0.010 agents=48 avg_r=-2.2743 sum_r=-582.23 x<0=0.07 elig=0.60 dorfler_tail=0.07 floor=0 sel=39 n_ref=0 r_loc=0.000 8.3s
+     3/401 | loss=0.6731 ev=0.019 agents=156 avg_r=-2.3457 sum_r=-600.50 x<0=0.07 elig=0.58 dorfler_tail=0.09 floor=0 sel=35 n_ref=0 r_loc=0.000 7.8s
+     4/401 | loss=1.1435 ev=0.036 agents=246 avg_r=-3.6846 sum_r=-943.26 x<0=0.05 elig=0.59 dorfler_tail=0.07 floor=0 sel=36 n_ref=0 r_loc=0.000 7.9s
+     5/401 | loss=0.6883 ev=0.056 agents=158 avg_r=-1.2686 sum_r=-324.77 x<0=0.05 elig=0.58 dorfler_tail=0.09 floor=0 sel=37 n_ref=0 r_loc=0.000 8.2s
+     6/401 | loss=0.9416 ev=0.095 agents=142 avg_r=-0.0596 sum_r=-15.24 x<0=0.04 elig=0.59 dorfler_tail=0.07 floor=0 sel=36 n_ref=0 r_loc=0.000 8.2s
+     7/401 | loss=0.7991 ev=0.105 agents=164 avg_r=-1.2996 sum_r=-332.70 x<0=0.03 elig=0.59 dorfler_tail=0.08 floor=0 sel=36 n_ref=0 r_loc=0.000 8.0s
+     8/401 | loss=0.7861 ev=0.117 agents=133 avg_r=-0.4898 sum_r=-125.39 x<0=0.02 elig=0.59 dorfler_tail=0.08 floor=0 sel=36 n_ref=0 r_loc=0.000 7.9s
+     9/401 | loss=0.7722 ev=0.141 agents=141 avg_r=-0.1621 sum_r=-41.50 x<0=0.02 elig=0.59 dorfler_tail=0.08 floor=0 sel=40 n_ref=0 r_loc=0.000 8.3s
+    10/401 | loss=1.0415 ev=0.134 agents=87 avg_r=-2.4506 sum_r=-627.35 x<0=0.02 elig=0.60 dorfler_tail=0.07 floor=0 sel=33 n_ref=0 r_loc=0.000 7.5s
+    11/401 | loss=0.6847 ev=0.166 agents=138 avg_r=-0.4086 sum_r=-104.60 x<0=0.01 elig=0.59 dorfler_tail=0.08 floor=0 sel=37 n_ref=0 r_loc=0.000 8.0s
+    12/401 | loss=0.6900 ev=0.146 agents=144 avg_r=1.5718 sum_r=402.39 x<0=0.01 elig=0.59 dorfler_tail=0.08 floor=0 sel=35 n_ref=0 r_loc=0.000 7.8s
+    13/401 | loss=0.9037 ev=0.191 agents=158 avg_r=-1.9889 sum_r=-509.15 x<0=0.01 elig=0.60 dorfler_tail=0.07 floor=0 sel=35 n_ref=0 r_loc=0.000 7.8s
+    14/401 | loss=0.7577 ev=0.175 agents=175 avg_r=-1.0029 sum_r=-256.74 x<0=0.01 elig=0.59 dorfler_tail=0.08 floor=0 sel=36 n_ref=0 r_loc=0.000 7.8s
+    15/401 | loss=0.6942 ev=0.208 agents=78 avg_r=-0.8006 sum_r=-204.95 x<0=0.01 elig=0.60 dorfler_tail=0.07 floor=0 sel=35 n_ref=0 r_loc=0.000 7.9s
+    16/401 | loss=0.8176 ev=0.205 agents=219 avg_r=1.1625 sum_r=297.59 x<0=0.01 elig=0.59 dorfler_tail=0.08 floor=0 sel=37 n_ref=0 r_loc=0.000 7.9s
+    17/401 | loss=0.5844 ev=0.178 agents=66 avg_r=-0.4453 sum_r=-114.01 x<0=0.00 elig=0.59 dorfler_tail=0.08 floor=0 sel=35 n_ref=0 r_loc=0.000 7.8s
+    18/401 | loss=0.9272 ev=0.198 agents=244 avg_r=-2.4742 sum_r=-633.40 x<0=0.01 elig=0.60 dorfler_tail=0.07 floor=0 sel=35 n_ref=0 r_loc=0.000 7.8s
+    19/401 | loss=0.6133 ev=0.215 agents=34 avg_r=-1.0759 sum_r=-275.42 x<0=0.01 elig=0.59 dorfler_tail=0.08 floor=0 sel=33 n_ref=0 r_loc=0.000 7.6s
+    20/401 | loss=0.7286 ev=0.260 agents=86 avg_r=2.3332 sum_r=597.30 x<0=0.01 elig=0.60 dorfler_tail=0.07 floor=0 sel=37 n_ref=0 r_loc=0.000 7.9s
+    21/401 | loss=0.6750 ev=0.250 agents=102 avg_r=-0.5468 sum_r=-139.98 x<0=0.01 elig=0.59 dorfler_tail=0.08 floor=0 sel=36 n_ref=0 r_loc=0.000 7.8s
+    22/401 | loss=0.6968 ev=0.188 agents=133 avg_r=-0.2165 sum_r=-55.43 x<0=0.01 elig=0.60 dorfler_tail=0.07 floor=0 sel=35 n_ref=0 r_loc=0.000 7.6s
+    23/401 | loss=0.6547 ev=0.251 agents=142 avg_r=0.7932 sum_r=203.07 x<0=0.01 elig=0.60 dorfler_tail=0.07 floor=0 sel=34 n_ref=0 r_loc=0.000 7.6s
+    24/401 | loss=0.7206 ev=0.221 agents=82 avg_r=-0.2919 sum_r=-74.74 x<0=0.01 elig=0.60 dorfler_tail=0.07 floor=0 sel=35 n_ref=0 r_loc=0.000 7.7s
+    25/401 | loss=0.6633 ev=0.305 agents=235 avg_r=1.9655 sum_r=503.16 x<0=0.01 elig=0.60 dorfler_tail=0.07 floor=0 sel=37 n_ref=0 r_loc=0.000 7.8s
+    26/401 | loss=0.7285 ev=0.215 agents=235 avg_r=-0.9946 sum_r=-254.60 x<0=0.00 elig=0.60 dorfler_tail=0.07 floor=0 sel=33 n_ref=0 r_loc=0.000 7.4s
+    27/401 | loss=0.6501 ev=0.264 agents=75 avg_r=-1.4324 sum_r=-366.69 x<0=0.01 elig=0.60 dorfler_tail=0.07 floor=0 sel=35 n_ref=0 r_loc=0.000 7.6s
+    28/401 | loss=0.5842 ev=0.262 agents=34 avg_r=0.2413 sum_r=61.77 x<0=0.01 elig=0.59 dorfler_tail=0.08 floor=0 sel=36 n_ref=0 r_loc=0.000 7.7s
+    29/401 | loss=0.7681 ev=0.295 agents=133 avg_r=0.3315 sum_r=84.86 x<0=0.01 elig=0.60 dorfler_tail=0.07 floor=0 sel=33 n_ref=0 r_loc=0.000 7.9s
+    30/401 | loss=0.8179 ev=0.292 agents=133 avg_r=0.4571 sum_r=117.01 x<0=0.01 elig=0.60 dorfler_tail=0.07 floor=0 sel=37 n_ref=0 r_loc=0.000 8.3s
+    31/401 | loss=0.6542 ev=0.232 agents=131 avg_r=1.6268 sum_r=416.47 x<0=0.01 elig=0.60 dorfler_tail=0.07 floor=0 sel=33 n_ref=0 r_loc=0.000 7.7s
+    32/401 | loss=0.5766 ev=0.204 agents=195 avg_r=-0.2509 sum_r=-64.23 x<0=0.02 elig=0.59 dorfler_tail=0.07 floor=0 sel=34 n_ref=0 r_loc=0.000 7.7s
+    33/401 | loss=0.6403 ev=0.237 agents=48 avg_r=3.0437 sum_r=779.18 x<0=0.02 elig=0.60 dorfler_tail=0.07 floor=0 sel=34 n_ref=0 r_loc=0.000 7.6s
+    34/401 | loss=0.7453 ev=0.291 agents=66 avg_r=-0.5863 sum_r=-150.09 x<0=0.01 elig=0.60 dorfler_tail=0.07 floor=0 sel=34 n_ref=0 r_loc=0.000 7.6s
+    35/401 | loss=0.6467 ev=0.303 agents=138 avg_r=1.6192 sum_r=414.51 x<0=0.02 elig=0.60 dorfler_tail=0.07 floor=0 sel=34 n_ref=0 r_loc=0.000 7.7s
+    36/401 | loss=0.6302 ev=0.289 agents=64 avg_r=1.1951 sum_r=305.96 x<0=0.01 elig=0.60 dorfler_tail=0.07 floor=0 sel=35 n_ref=0 r_loc=0.000 7.7s
+    37/401 | loss=0.7351 ev=0.301 agents=34 avg_r=-0.3947 sum_r=-101.03 x<0=0.01 elig=0.60 dorfler_tail=0.06 floor=0 sel=33 n_ref=0 r_loc=0.000 7.6s
+    38/401 | loss=0.6007 ev=0.312 agents=246 avg_r=0.4709 sum_r=120.55 x<0=0.01 elig=0.60 dorfler_tail=0.07 floor=0 sel=34 n_ref=0 r_loc=0.000 7.6s
+    39/401 | loss=0.6316 ev=0.318 agents=138 avg_r=1.0463 sum_r=267.85 x<0=0.01 elig=0.60 dorfler_tail=0.07 floor=0 sel=34 n_ref=0 r_loc=0.000 7.6s
+    40/401 | loss=0.6016 ev=0.143 agents=34 avg_r=1.0658 sum_r=272.85 x<0=0.01 elig=0.60 dorfler_tail=0.07 floor=0 sel=31 n_ref=0 r_loc=0.000 7.3s
+    41/401 | loss=0.7033 ev=0.306 agents=60 avg_r=3.5062 sum_r=897.59 x<0=0.01 elig=0.60 dorfler_tail=0.06 floor=0 sel=37 n_ref=0 r_loc=0.000 7.8s
+    42/401 | loss=0.5702 ev=0.268 agents=175 avg_r=-0.2759 sum_r=-70.64 x<0=0.01 elig=0.60 dorfler_tail=0.07 floor=0 sel=33 n_ref=0 r_loc=0.000 7.5s
+    43/401 | loss=0.5907 ev=0.324 agents=247 avg_r=0.7705 sum_r=197.25 x<0=0.01 elig=0.60 dorfler_tail=0.07 floor=0 sel=33 n_ref=0 r_loc=0.000 7.5s
+    44/401 | loss=0.6398 ev=0.306 agents=48 avg_r=1.4337 sum_r=367.03 x<0=0.01 elig=0.60 dorfler_tail=0.07 floor=0 sel=34 n_ref=0 r_loc=0.000 7.6s
+    45/401 | loss=0.6173 ev=0.266 agents=34 avg_r=0.4788 sum_r=122.56 x<0=0.00 elig=0.60 dorfler_tail=0.07 floor=0 sel=35 n_ref=0 r_loc=0.000 7.7s
+    46/401 | loss=0.5942 ev=0.262 agents=244 avg_r=0.2944 sum_r=75.38 x<0=0.01 elig=0.60 dorfler_tail=0.06 floor=0 sel=32 n_ref=0 r_loc=0.000 7.5s
+    47/401 | loss=0.6930 ev=0.312 agents=86 avg_r=2.0645 sum_r=528.51 x<0=0.01 elig=0.60 dorfler_tail=0.07 floor=0 sel=35 n_ref=0 r_loc=0.000 7.8s
+    48/401 | loss=0.6166 ev=0.265 agents=242 avg_r=-1.3247 sum_r=-339.13 x<0=0.01 elig=0.60 dorfler_tail=0.07 floor=0 sel=33 n_ref=0 r_loc=0.000 7.5s
+    49/401 | loss=0.6950 ev=0.281 agents=76 avg_r=0.5565 sum_r=142.46 x<0=0.01 elig=0.60 dorfler_tail=0.07 floor=0 sel=32 n_ref=0 r_loc=0.000 7.4s
+    50/401 | loss=0.5718 ev=0.306 agents=280 avg_r=1.5020 sum_r=384.52 x<0=0.01 elig=0.60 dorfler_tail=0.07 floor=0 sel=33 n_ref=0 r_loc=0.000 7.5s
+[Checkpoint] saved → checkpoints/model_iter0050.pt
+    51/401 | loss=0.5765 ev=0.337 agents=48 avg_r=1.0395 sum_r=266.11 x<0=0.01 elig=0.60 dorfler_tail=0.07 floor=0 sel=32 n_ref=0 r_loc=0.000 7.4s
+    52/401 | loss=0.7324 ev=0.326 agents=34 avg_r=-0.5879 sum_r=-150.50 x<0=0.01 elig=0.60 dorfler_tail=0.07 floor=0 sel=34 n_ref=0 r_loc=0.000 8.1s
+    53/401 | loss=0.6879 ev=0.195 agents=133 avg_r=0.2283 sum_r=58.44 x<0=0.01 elig=0.60 dorfler_tail=0.07 floor=0 sel=35 n_ref=0 r_loc=0.000 7.9s
+    54/401 | loss=0.5093 ev=0.354 agents=34 avg_r=3.4100 sum_r=872.97 x<0=0.01 elig=0.60 dorfler_tail=0.07 floor=0 sel=32 n_ref=0 r_loc=0.000 7.6s
+    55/401 | loss=0.5717 ev=0.241 agents=76 avg_r=0.1396 sum_r=35.73 x<0=0.01 elig=0.60 dorfler_tail=0.07 floor=0 sel=32 n_ref=0 r_loc=0.000 7.5s
+    56/401 | loss=0.6966 ev=0.329 agents=55 avg_r=1.8220 sum_r=466.43 x<0=0.02 elig=0.60 dorfler_tail=0.07 floor=0 sel=35 n_ref=0 r_loc=0.000 7.7s
+    57/401 | loss=0.6618 ev=0.271 agents=53 avg_r=0.1718 sum_r=43.99 x<0=0.01 elig=0.60 dorfler_tail=0.07 floor=0 sel=33 n_ref=0 r_loc=0.000 7.4s
+    58/401 | loss=0.7686 ev=0.308 agents=34 avg_r=-0.3162 sum_r=-80.94 x<0=0.02 elig=0.60 dorfler_tail=0.07 floor=0 sel=33 n_ref=0 r_loc=0.000 7.5s
+    59/401 | loss=0.6369 ev=0.282 agents=34 avg_r=1.1943 sum_r=305.74 x<0=0.02 elig=0.60 dorfler_tail=0.07 floor=0 sel=35 n_ref=0 r_loc=0.000 7.7s
+    60/401 | loss=0.5711 ev=0.316 agents=78 avg_r=0.4311 sum_r=110.36 x<0=0.02 elig=0.60 dorfler_tail=0.07 floor=0 sel=32 n_ref=0 r_loc=0.000 7.5s
+    61/401 | loss=0.6055 ev=0.243 agents=141 avg_r=0.7018 sum_r=179.65 x<0=0.02 elig=0.60 dorfler_tail=0.07 floor=0 sel=34 n_ref=0 r_loc=0.000 7.6s
+    62/401 | loss=0.5890 ev=0.320 agents=161 avg_r=2.4707 sum_r=632.49 x<0=0.02 elig=0.60 dorfler_tail=0.07 floor=0 sel=33 n_ref=0 r_loc=0.000 7.4s
+    63/401 | loss=0.7483 ev=0.299 agents=94 avg_r=-0.1036 sum_r=-26.52 x<0=0.02 elig=0.61 dorfler_tail=0.06 floor=0 sel=33 n_ref=0 r_loc=0.000 7.5s
+    64/401 | loss=0.5846 ev=0.308 agents=142 avg_r=2.2134 sum_r=566.62 x<0=0.03 elig=0.60 dorfler_tail=0.07 floor=0 sel=34 n_ref=0 r_loc=0.000 7.6s
+    65/401 | loss=0.6235 ev=0.310 agents=34 avg_r=0.3583 sum_r=91.72 x<0=0.03 elig=0.60 dorfler_tail=0.07 floor=0 sel=33 n_ref=0 r_loc=0.000 7.5s
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+[Checkpoint] saved → checkpoints/model_iter0100.pt
+   101/401 | loss=0.6111 ev=0.312 agents=87 avg_r=-1.0703 sum_r=-274.00 x<0=0.26 elig=0.61 dorfler_tail=0.07 floor=0 sel=33 n_ref=0 r_loc=0.000 7.5s
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+   146/401 | loss=0.6959 ev=0.388 agents=151 avg_r=0.5241 sum_r=134.16 x<0=0.23 elig=0.61 dorfler_tail=0.07 floor=0 sel=34 n_ref=0 r_loc=0.000 7.4s
+   147/401 | loss=0.5916 ev=0.367 agents=226 avg_r=1.0964 sum_r=280.67 x<0=0.21 elig=0.61 dorfler_tail=0.06 floor=0 sel=31 n_ref=0 r_loc=0.000 7.7s
+   148/401 | loss=0.6063 ev=0.321 agents=549 avg_r=-1.3176 sum_r=-337.29 x<0=0.22 elig=0.60 dorfler_tail=0.06 floor=0 sel=31 n_ref=0 r_loc=0.000 7.4s
+   149/401 | loss=0.5880 ev=0.369 agents=144 avg_r=-0.5012 sum_r=-128.32 x<0=0.23 elig=0.61 dorfler_tail=0.07 floor=0 sel=32 n_ref=0 r_loc=0.000 7.5s
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+[Checkpoint] saved → checkpoints/model_iter0150.pt
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+[Checkpoint] saved → checkpoints/model_iter0200.pt
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+[Checkpoint] saved → checkpoints/model_iter0250.pt
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+   299/401 | loss=0.4948 ev=0.320 agents=34 avg_r=0.1841 sum_r=47.12 x<0=0.25 elig=0.61 dorfler_tail=0.07 floor=0 sel=32 n_ref=0 r_loc=0.000 7.3s
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+[Checkpoint] saved → checkpoints/model_iter0300.pt
+   301/401 | loss=0.6045 ev=0.323 agents=556 avg_r=-0.8391 sum_r=-214.80 x<0=0.25 elig=0.61 dorfler_tail=0.07 floor=0 sel=31 n_ref=0 r_loc=0.000 7.2s
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+   347/401 | loss=0.4937 ev=0.428 agents=217 avg_r=-1.5564 sum_r=-398.43 x<0=0.24 elig=0.61 dorfler_tail=0.07 floor=0 sel=31 n_ref=0 r_loc=0.000 7.3s
+   348/401 | loss=0.5818 ev=0.337 agents=72 avg_r=-1.5159 sum_r=-388.07 x<0=0.26 elig=0.62 dorfler_tail=0.06 floor=0 sel=30 n_ref=0 r_loc=0.000 7.2s
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+[Checkpoint] saved → checkpoints/model_iter0350.pt
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+   355/401 | loss=0.5905 ev=0.379 agents=1077 avg_r=-2.1700 sum_r=-555.53 x<0=0.26 elig=0.62 dorfler_tail=0.07 floor=0 sel=33 n_ref=0 r_loc=0.000 8.0s
+   356/401 | loss=0.5469 ev=0.389 agents=140 avg_r=-1.3158 sum_r=-336.85 x<0=0.26 elig=0.61 dorfler_tail=0.07 floor=0 sel=31 n_ref=0 r_loc=0.000 7.6s
+   357/401 | loss=0.5095 ev=0.397 agents=764 avg_r=-0.0966 sum_r=-24.72 x<0=0.24 elig=0.61 dorfler_tail=0.07 floor=0 sel=32 n_ref=0 r_loc=0.000 7.7s
+   358/401 | loss=0.5770 ev=0.395 agents=125 avg_r=-2.5987 sum_r=-665.27 x<0=0.25 elig=0.61 dorfler_tail=0.07 floor=0 sel=30 n_ref=0 r_loc=0.000 7.4s
+   359/401 | loss=0.6685 ev=0.406 agents=103 avg_r=-3.2896 sum_r=-842.13 x<0=0.23 elig=0.63 dorfler_tail=0.06 floor=0 sel=29 n_ref=0 r_loc=0.000 7.2s
+   360/401 | loss=0.5382 ev=0.408 agents=537 avg_r=0.4558 sum_r=116.70 x<0=0.25 elig=0.61 dorfler_tail=0.07 floor=0 sel=34 n_ref=0 r_loc=0.000 7.7s
+   361/401 | loss=0.5846 ev=0.384 agents=245 avg_r=-1.1329 sum_r=-290.03 x<0=0.24 elig=0.62 dorfler_tail=0.06 floor=0 sel=30 n_ref=0 r_loc=0.000 7.3s
+   362/401 | loss=0.5318 ev=0.404 agents=194 avg_r=-1.1031 sum_r=-282.39 x<0=0.25 elig=0.61 dorfler_tail=0.06 floor=0 sel=31 n_ref=0 r_loc=0.000 7.3s
+   363/401 | loss=0.6778 ev=0.410 agents=155 avg_r=-3.5161 sum_r=-900.13 x<0=0.25 elig=0.63 dorfler_tail=0.07 floor=0 sel=33 n_ref=0 r_loc=0.000 7.8s
+   364/401 | loss=0.5592 ev=0.387 agents=720 avg_r=-3.1739 sum_r=-812.52 x<0=0.25 elig=0.61 dorfler_tail=0.06 floor=0 sel=29 n_ref=0 r_loc=0.000 7.2s
+   365/401 | loss=0.5257 ev=0.340 agents=195 avg_r=1.4110 sum_r=361.21 x<0=0.24 elig=0.61 dorfler_tail=0.07 floor=0 sel=33 n_ref=0 r_loc=0.000 7.5s
+   366/401 | loss=0.7202 ev=0.381 agents=64 avg_r=-3.0263 sum_r=-774.72 x<0=0.24 elig=0.62 dorfler_tail=0.06 floor=0 sel=30 n_ref=0 r_loc=0.000 7.2s
+   367/401 | loss=0.5865 ev=0.393 agents=584 avg_r=-2.2033 sum_r=-564.05 x<0=0.24 elig=0.62 dorfler_tail=0.07 floor=0 sel=31 n_ref=0 r_loc=0.000 7.4s
+   368/401 | loss=0.5074 ev=0.411 agents=78 avg_r=-2.5681 sum_r=-657.44 x<0=0.25 elig=0.62 dorfler_tail=0.07 floor=0 sel=32 n_ref=0 r_loc=0.000 7.4s
+   369/401 | loss=0.5519 ev=0.377 agents=183 avg_r=0.4932 sum_r=126.27 x<0=0.25 elig=0.62 dorfler_tail=0.07 floor=0 sel=31 n_ref=0 r_loc=0.000 7.4s
+   370/401 | loss=0.5265 ev=0.397 agents=183 avg_r=-1.9064 sum_r=-488.03 x<0=0.24 elig=0.62 dorfler_tail=0.06 floor=0 sel=32 n_ref=0 r_loc=0.000 7.4s
+   371/401 | loss=0.6248 ev=0.468 agents=325 avg_r=-1.4349 sum_r=-367.34 x<0=0.23 elig=0.62 dorfler_tail=0.06 floor=0 sel=32 n_ref=0 r_loc=0.000 7.5s
+   372/401 | loss=0.6210 ev=0.368 agents=195 avg_r=-2.1573 sum_r=-552.26 x<0=0.24 elig=0.62 dorfler_tail=0.07 floor=0 sel=31 n_ref=0 r_loc=0.000 7.3s
+   373/401 | loss=0.5398 ev=0.381 agents=1257 avg_r=0.1999 sum_r=51.16 x<0=0.24 elig=0.61 dorfler_tail=0.07 floor=0 sel=33 n_ref=0 r_loc=0.000 7.5s
+   374/401 | loss=0.7041 ev=0.437 agents=140 avg_r=-2.6638 sum_r=-681.93 x<0=0.24 elig=0.63 dorfler_tail=0.06 floor=0 sel=28 n_ref=0 r_loc=0.000 7.0s
+   375/401 | loss=0.5560 ev=0.344 agents=1153 avg_r=-4.6746 sum_r=-1196.70 x<0=0.26 elig=0.62 dorfler_tail=0.06 floor=0 sel=33 n_ref=0 r_loc=0.000 7.6s
+   376/401 | loss=0.5135 ev=0.402 agents=145 avg_r=0.4112 sum_r=105.26 x<0=0.24 elig=0.62 dorfler_tail=0.06 floor=0 sel=29 n_ref=0 r_loc=0.000 7.1s
+   377/401 | loss=0.5797 ev=0.389 agents=476 avg_r=-1.3227 sum_r=-338.62 x<0=0.26 elig=0.62 dorfler_tail=0.07 floor=0 sel=33 n_ref=0 r_loc=0.000 7.6s
+   378/401 | loss=0.5229 ev=0.401 agents=80 avg_r=-1.8801 sum_r=-481.30 x<0=0.25 elig=0.62 dorfler_tail=0.06 floor=0 sel=30 n_ref=0 r_loc=0.000 7.3s
+   379/401 | loss=0.5683 ev=0.371 agents=94 avg_r=-2.1285 sum_r=-544.89 x<0=0.25 elig=0.62 dorfler_tail=0.06 floor=0 sel=33 n_ref=0 r_loc=0.000 8.0s
+   380/401 | loss=0.5654 ev=0.402 agents=196 avg_r=-2.9217 sum_r=-747.96 x<0=0.25 elig=0.62 dorfler_tail=0.07 floor=0 sel=30 n_ref=0 r_loc=0.000 7.6s
+   381/401 | loss=0.6029 ev=0.422 agents=76 avg_r=0.8416 sum_r=215.45 x<0=0.25 elig=0.63 dorfler_tail=0.06 floor=0 sel=30 n_ref=0 r_loc=0.000 7.6s
+   382/401 | loss=0.5868 ev=0.403 agents=202 avg_r=-3.3551 sum_r=-858.92 x<0=0.24 elig=0.62 dorfler_tail=0.07 floor=0 sel=33 n_ref=0 r_loc=0.000 7.8s
+   383/401 | loss=0.5493 ev=0.371 agents=759 avg_r=-1.1757 sum_r=-300.97 x<0=0.25 elig=0.62 dorfler_tail=0.07 floor=0 sel=30 n_ref=0 r_loc=0.000 7.4s
+   384/401 | loss=0.5628 ev=0.398 agents=286 avg_r=-2.6977 sum_r=-690.62 x<0=0.25 elig=0.62 dorfler_tail=0.07 floor=0 sel=31 n_ref=0 r_loc=0.000 7.5s
+   385/401 | loss=0.5984 ev=0.329 agents=79 avg_r=-0.9978 sum_r=-255.44 x<0=0.25 elig=0.62 dorfler_tail=0.06 floor=0 sel=30 n_ref=0 r_loc=0.000 7.4s
+   386/401 | loss=0.6295 ev=0.474 agents=112 avg_r=-2.3561 sum_r=-603.16 x<0=0.25 elig=0.63 dorfler_tail=0.06 floor=0 sel=32 n_ref=0 r_loc=0.000 7.6s
+   387/401 | loss=0.5699 ev=0.372 agents=747 avg_r=-2.0223 sum_r=-517.72 x<0=0.25 elig=0.61 dorfler_tail=0.07 floor=0 sel=31 n_ref=0 r_loc=0.000 7.4s
+   388/401 | loss=0.5713 ev=0.367 agents=74 avg_r=-2.6122 sum_r=-668.71 x<0=0.23 elig=0.63 dorfler_tail=0.06 floor=0 sel=30 n_ref=0 r_loc=0.000 7.4s
+   389/401 | loss=0.5408 ev=0.380 agents=34 avg_r=-0.7515 sum_r=-192.39 x<0=0.24 elig=0.62 dorfler_tail=0.07 floor=0 sel=32 n_ref=0 r_loc=0.000 7.5s
+   390/401 | loss=0.5509 ev=0.404 agents=185 avg_r=-1.0922 sum_r=-279.60 x<0=0.24 elig=0.62 dorfler_tail=0.07 floor=0 sel=31 n_ref=0 r_loc=0.000 7.5s
+   391/401 | loss=0.7629 ev=0.392 agents=1114 avg_r=-2.8317 sum_r=-724.91 x<0=0.24 elig=0.62 dorfler_tail=0.06 floor=0 sel=30 n_ref=0 r_loc=0.000 7.2s
+   392/401 | loss=0.5248 ev=0.384 agents=204 avg_r=0.4260 sum_r=109.06 x<0=0.24 elig=0.62 dorfler_tail=0.07 floor=0 sel=33 n_ref=0 r_loc=0.000 7.7s
+   393/401 | loss=0.5672 ev=0.383 agents=84 avg_r=-1.4752 sum_r=-377.66 x<0=0.25 elig=0.62 dorfler_tail=0.07 floor=0 sel=30 n_ref=0 r_loc=0.000 7.3s
+   394/401 | loss=0.5358 ev=0.420 agents=136 avg_r=-2.7112 sum_r=-694.07 x<0=0.24 elig=0.62 dorfler_tail=0.07 floor=0 sel=32 n_ref=0 r_loc=0.000 7.5s
+   395/401 | loss=0.5721 ev=0.385 agents=123 avg_r=-0.5855 sum_r=-149.88 x<0=0.25 elig=0.62 dorfler_tail=0.07 floor=0 sel=32 n_ref=0 r_loc=0.000 7.5s
+   396/401 | loss=0.6814 ev=0.430 agents=769 avg_r=-2.4388 sum_r=-624.33 x<0=0.25 elig=0.62 dorfler_tail=0.06 floor=0 sel=30 n_ref=0 r_loc=0.000 7.3s
+   397/401 | loss=0.4945 ev=0.420 agents=196 avg_r=-1.5640 sum_r=-400.38 x<0=0.24 elig=0.62 dorfler_tail=0.07 floor=0 sel=32 n_ref=0 r_loc=0.000 7.6s
+   398/401 | loss=0.5281 ev=0.308 agents=179 avg_r=-1.0618 sum_r=-271.83 x<0=0.24 elig=0.62 dorfler_tail=0.07 floor=0 sel=30 n_ref=0 r_loc=0.000 7.2s
+   399/401 | loss=0.7013 ev=0.408 agents=177 avg_r=-3.2987 sum_r=-844.47 x<0=0.24 elig=0.62 dorfler_tail=0.06 floor=0 sel=30 n_ref=0 r_loc=0.000 7.4s
+   400/401 | loss=0.5656 ev=0.374 agents=1732 avg_r=-1.8509 sum_r=-473.83 x<0=0.24 elig=0.62 dorfler_tail=0.06 floor=0 sel=31 n_ref=0 r_loc=0.000 7.3s
+[Checkpoint] saved → checkpoints/model_iter0400.pt
+   401/401 | loss=0.5597 ev=0.432 agents=220 avg_r=-2.2646 sum_r=-579.72 x<0=0.24 elig=0.62 dorfler_tail=0.06 floor=0 sel=31 n_ref=0 r_loc=0.000 7.4s
+[Checkpoint] saved → checkpoints/model_iter0401.pt
+[Checkpoint] saved → checkpoints/model_final.pt
+[Train] done, total time 2975.5s
+Training finished at Thu 28 May 14:15:44 CST 2026
diff --git a/logs/stop150.out b/logs/stop150.out
new file mode 100644
index 0000000..8595bbc
--- /dev/null
+++ b/logs/stop150.out
@@ -0,0 +1,178 @@
+Starting training at Fri 29 May 14:36:05 CST 2026
+Running on node: node06
+[Device] cuda
+[Env] node_feats=14 edge_feats=1 act_dim=1
+[Model] params=92,804
+     1/401 | loss=1.2593 ev=-0.005 agents=109 avg_r=-0.4716 sum_r=-120.74 x<0=0.69 elig=0.58 dorfler_tail=0.09 floor=0 sel=35 8.7s
+     2/401 | loss=1.1660 ev=0.023 agents=193 avg_r=1.8712 sum_r=479.03 x<0=0.62 elig=0.58 dorfler_tail=0.08 floor=0 sel=32 7.8s
+     3/401 | loss=1.1102 ev=0.044 agents=39 avg_r=-1.2724 sum_r=-325.74 x<0=0.60 elig=0.59 dorfler_tail=0.08 floor=0 sel=32 7.8s
+     4/401 | loss=1.1780 ev=0.065 agents=34 avg_r=2.1552 sum_r=551.73 x<0=0.61 elig=0.58 dorfler_tail=0.09 floor=0 sel=35 8.3s
+     5/401 | loss=1.1065 ev=0.091 agents=88 avg_r=-1.4642 sum_r=-374.83 x<0=0.52 elig=0.59 dorfler_tail=0.08 floor=0 sel=32 8.0s
+     6/401 | loss=1.2564 ev=0.098 agents=36 avg_r=1.5516 sum_r=397.20 x<0=0.49 elig=0.59 dorfler_tail=0.08 floor=0 sel=32 7.8s
+     7/401 | loss=1.0063 ev=0.172 agents=34 avg_r=0.8841 sum_r=226.33 x<0=0.47 elig=0.58 dorfler_tail=0.09 floor=0 sel=35 8.1s
+     8/401 | loss=1.3696 ev=0.168 agents=133 avg_r=0.6858 sum_r=175.58 x<0=0.44 elig=0.59 dorfler_tail=0.08 floor=0 sel=33 7.9s
+     9/401 | loss=1.1844 ev=0.215 agents=79 avg_r=0.2644 sum_r=67.68 x<0=0.45 elig=0.59 dorfler_tail=0.08 floor=0 sel=31 7.7s
+    10/401 | loss=1.0413 ev=0.216 agents=82 avg_r=-1.0025 sum_r=-256.64 x<0=0.42 elig=0.59 dorfler_tail=0.08 floor=0 sel=34 8.0s
+    11/401 | loss=1.2795 ev=0.256 agents=60 avg_r=2.6849 sum_r=687.34 x<0=0.39 elig=0.59 dorfler_tail=0.08 floor=0 sel=31 7.8s
+    12/401 | loss=0.8503 ev=0.306 agents=48 avg_r=0.5254 sum_r=134.49 x<0=0.40 elig=0.59 dorfler_tail=0.08 floor=0 sel=33 7.9s
+    13/401 | loss=0.8283 ev=0.322 agents=88 avg_r=0.9044 sum_r=231.52 x<0=0.42 elig=0.58 dorfler_tail=0.08 floor=0 sel=33 7.9s
+    14/401 | loss=0.8950 ev=0.298 agents=40 avg_r=0.4961 sum_r=127.00 x<0=0.39 elig=0.59 dorfler_tail=0.08 floor=0 sel=33 7.9s
+    15/401 | loss=0.8561 ev=0.342 agents=101 avg_r=0.5456 sum_r=139.67 x<0=0.41 elig=0.58 dorfler_tail=0.08 floor=0 sel=34 8.0s
+    16/401 | loss=1.1581 ev=0.283 agents=34 avg_r=-1.9177 sum_r=-490.92 x<0=0.33 elig=0.59 dorfler_tail=0.08 floor=0 sel=29 7.5s
+    17/401 | loss=0.8868 ev=0.364 agents=132 avg_r=3.2843 sum_r=840.77 x<0=0.33 elig=0.59 dorfler_tail=0.08 floor=0 sel=33 8.0s
+    18/401 | loss=0.8571 ev=0.349 agents=34 avg_r=1.1258 sum_r=288.21 x<0=0.30 elig=0.58 dorfler_tail=0.08 floor=0 sel=32 7.9s
+    19/401 | loss=0.7991 ev=0.374 agents=201 avg_r=-0.2317 sum_r=-59.32 x<0=0.28 elig=0.59 dorfler_tail=0.08 floor=0 sel=35 8.1s
+    20/401 | loss=0.8149 ev=0.386 agents=120 avg_r=1.5704 sum_r=402.02 x<0=0.21 elig=0.59 dorfler_tail=0.08 floor=0 sel=31 7.7s
+    21/401 | loss=0.8764 ev=0.357 agents=78 avg_r=0.5421 sum_r=138.78 x<0=0.22 elig=0.59 dorfler_tail=0.08 floor=0 sel=32 7.7s
+    22/401 | loss=0.7788 ev=0.367 agents=44 avg_r=0.6768 sum_r=173.27 x<0=0.17 elig=0.59 dorfler_tail=0.08 floor=0 sel=32 7.7s
+    23/401 | loss=0.7429 ev=0.382 agents=36 avg_r=0.6276 sum_r=160.68 x<0=0.16 elig=0.59 dorfler_tail=0.08 floor=0 sel=32 7.8s
+    24/401 | loss=0.8267 ev=0.404 agents=175 avg_r=3.4114 sum_r=873.33 x<0=0.13 elig=0.59 dorfler_tail=0.08 floor=0 sel=33 7.9s
+    25/401 | loss=0.7211 ev=0.390 agents=34 avg_r=0.2581 sum_r=66.07 x<0=0.12 elig=0.59 dorfler_tail=0.08 floor=0 sel=29 7.4s
+    26/401 | loss=0.9829 ev=0.350 agents=34 avg_r=-0.0098 sum_r=-2.50 x<0=0.13 elig=0.59 dorfler_tail=0.08 floor=0 sel=34 8.0s
+    27/401 | loss=0.7973 ev=0.356 agents=176 avg_r=0.8028 sum_r=205.51 x<0=0.12 elig=0.59 dorfler_tail=0.08 floor=0 sel=31 8.1s
+    28/401 | loss=0.7603 ev=0.414 agents=219 avg_r=0.7955 sum_r=203.65 x<0=0.10 elig=0.59 dorfler_tail=0.08 floor=0 sel=32 8.1s
+    29/401 | loss=0.7585 ev=0.375 agents=44 avg_r=1.5867 sum_r=406.19 x<0=0.09 elig=0.59 dorfler_tail=0.08 floor=0 sel=32 8.0s
+    30/401 | loss=0.6940 ev=0.425 agents=133 avg_r=2.4328 sum_r=622.81 x<0=0.09 elig=0.59 dorfler_tail=0.08 floor=0 sel=30 7.6s
+    31/401 | loss=0.9083 ev=0.370 agents=44 avg_r=2.5351 sum_r=648.99 x<0=0.13 elig=0.59 dorfler_tail=0.08 floor=0 sel=32 7.8s
+    32/401 | loss=1.0825 ev=0.356 agents=34 avg_r=0.0954 sum_r=24.43 x<0=0.16 elig=0.59 dorfler_tail=0.08 floor=0 sel=33 8.0s
+    33/401 | loss=0.6799 ev=0.430 agents=752 avg_r=2.1090 sum_r=539.90 x<0=0.15 elig=0.59 dorfler_tail=0.07 floor=0 sel=31 7.7s
+    34/401 | loss=1.0309 ev=0.325 agents=132 avg_r=-0.3870 sum_r=-99.07 x<0=0.14 elig=0.60 dorfler_tail=0.07 floor=0 sel=31 7.6s
+    35/401 | loss=0.7810 ev=0.385 agents=60 avg_r=2.1370 sum_r=547.06 x<0=0.10 elig=0.59 dorfler_tail=0.08 floor=0 sel=31 7.5s
+    36/401 | loss=0.7733 ev=0.381 agents=139 avg_r=0.5555 sum_r=142.22 x<0=0.09 elig=0.59 dorfler_tail=0.08 floor=0 sel=29 7.4s
+    37/401 | loss=0.7242 ev=0.386 agents=752 avg_r=1.7036 sum_r=436.12 x<0=0.10 elig=0.59 dorfler_tail=0.07 floor=0 sel=31 7.5s
+    38/401 | loss=0.7454 ev=0.402 agents=34 avg_r=1.7798 sum_r=455.64 x<0=0.09 elig=0.59 dorfler_tail=0.07 floor=0 sel=31 7.5s
+    39/401 | loss=0.6106 ev=0.445 agents=87 avg_r=2.2153 sum_r=567.13 x<0=0.06 elig=0.60 dorfler_tail=0.08 floor=0 sel=30 7.5s
+    40/401 | loss=0.8085 ev=0.381 agents=88 avg_r=2.2893 sum_r=586.06 x<0=0.06 elig=0.59 dorfler_tail=0.08 floor=0 sel=33 7.7s
+    41/401 | loss=0.6706 ev=0.419 agents=301 avg_r=1.4149 sum_r=362.21 x<0=0.05 elig=0.59 dorfler_tail=0.07 floor=0 sel=29 7.2s
+    42/401 | loss=0.6504 ev=0.440 agents=1563 avg_r=2.3614 sum_r=604.52 x<0=0.06 elig=0.59 dorfler_tail=0.07 floor=0 sel=31 7.5s
+    43/401 | loss=0.6548 ev=0.389 agents=905 avg_r=2.1166 sum_r=541.85 x<0=0.05 elig=0.59 dorfler_tail=0.08 floor=0 sel=30 7.5s
+    44/401 | loss=0.6763 ev=0.392 agents=603 avg_r=2.1965 sum_r=562.30 x<0=0.05 elig=0.60 dorfler_tail=0.08 floor=0 sel=31 7.6s
+    45/401 | loss=0.6371 ev=0.417 agents=321 avg_r=1.2079 sum_r=309.23 x<0=0.04 elig=0.59 dorfler_tail=0.07 floor=0 sel=29 7.3s
+    46/401 | loss=0.7580 ev=0.419 agents=64 avg_r=2.3964 sum_r=613.47 x<0=0.05 elig=0.59 dorfler_tail=0.07 floor=0 sel=31 7.6s
+    47/401 | loss=0.8826 ev=0.357 agents=648 avg_r=1.9237 sum_r=492.46 x<0=0.07 elig=0.60 dorfler_tail=0.08 floor=0 sel=30 7.4s
+    48/401 | loss=0.7618 ev=0.374 agents=72 avg_r=1.9302 sum_r=494.14 x<0=0.04 elig=0.59 dorfler_tail=0.07 floor=0 sel=31 7.4s
+    49/401 | loss=1.0496 ev=0.349 agents=1113 avg_r=1.6100 sum_r=412.15 x<0=0.05 elig=0.59 dorfler_tail=0.07 floor=0 sel=31 8.0s
+    50/401 | loss=1.0966 ev=0.355 agents=207 avg_r=0.2694 sum_r=68.96 x<0=0.04 elig=0.59 dorfler_tail=0.07 floor=0 sel=30 7.7s
+[Checkpoint] saved → checkpoints/model_iter0050.pt
+    51/401 | loss=0.7497 ev=0.362 agents=88 avg_r=2.4859 sum_r=636.39 x<0=0.04 elig=0.59 dorfler_tail=0.07 floor=0 sel=30 7.6s
+    52/401 | loss=0.7117 ev=0.376 agents=34 avg_r=1.3932 sum_r=356.65 x<0=0.04 elig=0.60 dorfler_tail=0.07 floor=0 sel=29 7.5s
+    53/401 | loss=0.8732 ev=0.428 agents=482 avg_r=2.5241 sum_r=646.16 x<0=0.05 elig=0.60 dorfler_tail=0.07 floor=0 sel=30 7.5s
+    54/401 | loss=0.7275 ev=0.414 agents=797 avg_r=2.5614 sum_r=655.71 x<0=0.03 elig=0.60 dorfler_tail=0.07 floor=0 sel=31 7.6s
+    55/401 | loss=1.0015 ev=0.267 agents=238 avg_r=1.7553 sum_r=449.35 x<0=0.03 elig=0.60 dorfler_tail=0.07 floor=0 sel=31 7.7s
+    56/401 | loss=0.9532 ev=0.328 agents=78 avg_r=1.6596 sum_r=424.86 x<0=0.04 elig=0.61 dorfler_tail=0.07 floor=0 sel=27 7.3s
+    57/401 | loss=0.9659 ev=0.392 agents=180 avg_r=0.1315 sum_r=33.67 x<0=0.04 elig=0.60 dorfler_tail=0.07 floor=0 sel=30 7.6s
+    58/401 | loss=0.5575 ev=0.479 agents=1467 avg_r=3.9607 sum_r=1013.94 x<0=0.04 elig=0.59 dorfler_tail=0.08 floor=0 sel=31 7.6s
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+    72/401 | loss=0.6831 ev=0.418 agents=84 avg_r=2.0187 sum_r=516.80 x<0=0.01 elig=0.61 dorfler_tail=0.07 floor=0 sel=28 7.8s
+    73/401 | loss=0.7298 ev=0.426 agents=438 avg_r=2.5987 sum_r=665.26 x<0=0.00 elig=0.60 dorfler_tail=0.07 floor=0 sel=30 7.7s
+    74/401 | loss=0.6047 ev=0.470 agents=301 avg_r=3.4593 sum_r=885.58 x<0=0.00 elig=0.60 dorfler_tail=0.07 floor=0 sel=29 7.6s
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+    76/401 | loss=0.9368 ev=0.393 agents=503 avg_r=2.7642 sum_r=707.63 x<0=0.00 elig=0.60 dorfler_tail=0.07 floor=0 sel=30 7.7s
+    77/401 | loss=0.9459 ev=0.432 agents=261 avg_r=1.2000 sum_r=307.20 x<0=0.01 elig=0.60 dorfler_tail=0.07 floor=0 sel=28 7.3s
+    78/401 | loss=0.7438 ev=0.411 agents=221 avg_r=2.1195 sum_r=542.58 x<0=0.00 elig=0.61 dorfler_tail=0.07 floor=0 sel=30 7.6s
+    79/401 | loss=0.7466 ev=0.450 agents=232 avg_r=4.4824 sum_r=1147.50 x<0=0.01 elig=0.60 dorfler_tail=0.08 floor=0 sel=32 7.7s
+    80/401 | loss=1.1380 ev=0.460 agents=814 avg_r=0.3357 sum_r=85.95 x<0=0.01 elig=0.61 dorfler_tail=0.07 floor=0 sel=27 7.2s
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+    82/401 | loss=0.5936 ev=0.436 agents=237 avg_r=3.5513 sum_r=909.14 x<0=0.00 elig=0.60 dorfler_tail=0.07 floor=0 sel=29 7.5s
+    83/401 | loss=0.6978 ev=0.432 agents=389 avg_r=2.7072 sum_r=693.05 x<0=0.00 elig=0.61 dorfler_tail=0.07 floor=0 sel=28 7.5s
+    84/401 | loss=0.8955 ev=0.404 agents=80 avg_r=3.3064 sum_r=846.43 x<0=0.00 elig=0.61 dorfler_tail=0.07 floor=0 sel=31 7.8s
+    85/401 | loss=0.8506 ev=0.432 agents=34 avg_r=0.2730 sum_r=69.89 x<0=0.00 elig=0.61 dorfler_tail=0.07 floor=0 sel=24 6.9s
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+    87/401 | loss=0.8894 ev=0.397 agents=418 avg_r=2.6888 sum_r=688.32 x<0=0.00 elig=0.62 dorfler_tail=0.07 floor=0 sel=28 7.5s
+    88/401 | loss=1.0689 ev=0.411 agents=80 avg_r=3.0347 sum_r=776.89 x<0=0.01 elig=0.62 dorfler_tail=0.07 floor=0 sel=28 7.6s
+    89/401 | loss=0.8925 ev=0.358 agents=862 avg_r=2.9356 sum_r=751.50 x<0=0.01 elig=0.62 dorfler_tail=0.07 floor=0 sel=29 7.8s
+    90/401 | loss=0.7441 ev=0.464 agents=549 avg_r=4.5978 sum_r=1177.04 x<0=0.01 elig=0.62 dorfler_tail=0.07 floor=0 sel=28 7.6s
+    91/401 | loss=1.1180 ev=0.386 agents=101 avg_r=2.1914 sum_r=560.99 x<0=0.00 elig=0.62 dorfler_tail=0.07 floor=0 sel=29 7.6s
+    92/401 | loss=0.9271 ev=0.439 agents=60 avg_r=3.2678 sum_r=836.57 x<0=0.00 elig=0.63 dorfler_tail=0.07 floor=0 sel=27 7.5s
+    93/401 | loss=0.9531 ev=0.437 agents=291 avg_r=3.1621 sum_r=809.49 x<0=0.00 elig=0.63 dorfler_tail=0.07 floor=0 sel=28 7.6s
+    94/401 | loss=0.8870 ev=0.439 agents=101 avg_r=3.1353 sum_r=802.65 x<0=0.00 elig=0.63 dorfler_tail=0.07 floor=0 sel=28 8.0s
+    95/401 | loss=0.9440 ev=0.434 agents=34 avg_r=5.3761 sum_r=1376.27 x<0=0.01 elig=0.63 dorfler_tail=0.07 floor=0 sel=30 8.4s
+    96/401 | loss=1.1221 ev=0.381 agents=62 avg_r=2.8338 sum_r=725.45 x<0=0.00 elig=0.63 dorfler_tail=0.07 floor=0 sel=28 7.9s
+    97/401 | loss=0.9903 ev=0.452 agents=180 avg_r=4.0017 sum_r=1024.43 x<0=0.00 elig=0.63 dorfler_tail=0.07 floor=0 sel=28 7.9s
+    98/401 | loss=1.0881 ev=0.436 agents=419 avg_r=4.6007 sum_r=1177.77 x<0=0.01 elig=0.63 dorfler_tail=0.07 floor=0 sel=29 7.9s
+    99/401 | loss=0.8982 ev=0.432 agents=85 avg_r=2.9775 sum_r=762.24 x<0=0.01 elig=0.63 dorfler_tail=0.07 floor=0 sel=28 7.8s
+   100/401 | loss=1.0656 ev=0.359 agents=691 avg_r=3.0152 sum_r=771.89 x<0=0.01 elig=0.63 dorfler_tail=0.07 floor=0 sel=28 7.7s
+[Checkpoint] saved → checkpoints/model_iter0100.pt
+   101/401 | loss=0.8757 ev=0.449 agents=147 avg_r=4.0589 sum_r=1039.07 x<0=0.00 elig=0.62 dorfler_tail=0.08 floor=0 sel=29 7.7s
+   102/401 | loss=0.9537 ev=0.441 agents=802 avg_r=4.1671 sum_r=1066.79 x<0=0.00 elig=0.62 dorfler_tail=0.07 floor=0 sel=29 7.7s
+   103/401 | loss=1.1348 ev=0.457 agents=120 avg_r=4.9407 sum_r=1264.81 x<0=0.00 elig=0.62 dorfler_tail=0.07 floor=0 sel=29 7.9s
+   104/401 | loss=1.0887 ev=0.415 agents=48 avg_r=3.7664 sum_r=964.21 x<0=0.01 elig=0.63 dorfler_tail=0.07 floor=0 sel=29 7.8s
+   105/401 | loss=0.7257 ev=0.441 agents=245 avg_r=1.1230 sum_r=287.49 x<0=0.00 elig=0.62 dorfler_tail=0.07 floor=0 sel=26 7.5s
+   106/401 | loss=0.9558 ev=0.429 agents=193 avg_r=3.9291 sum_r=1005.86 x<0=0.00 elig=0.63 dorfler_tail=0.07 floor=0 sel=28 7.7s
+   107/401 | loss=1.1960 ev=0.461 agents=140 avg_r=3.8453 sum_r=984.40 x<0=0.01 elig=0.63 dorfler_tail=0.07 floor=0 sel=29 8.0s
+   108/401 | loss=1.0023 ev=0.425 agents=34 avg_r=3.5098 sum_r=898.50 x<0=0.00 elig=0.63 dorfler_tail=0.07 floor=0 sel=26 7.5s
+   109/401 | loss=1.0553 ev=0.437 agents=155 avg_r=4.4515 sum_r=1139.58 x<0=0.00 elig=0.63 dorfler_tail=0.07 floor=0 sel=29 7.8s
+   110/401 | loss=0.8946 ev=0.458 agents=317 avg_r=2.2184 sum_r=567.91 x<0=0.00 elig=0.62 dorfler_tail=0.07 floor=0 sel=28 7.6s
+   111/401 | loss=0.8399 ev=0.475 agents=322 avg_r=3.8648 sum_r=989.39 x<0=0.00 elig=0.63 dorfler_tail=0.07 floor=0 sel=28 7.6s
+   112/401 | loss=0.8203 ev=0.450 agents=661 avg_r=4.3269 sum_r=1107.69 x<0=0.01 elig=0.63 dorfler_tail=0.07 floor=0 sel=29 7.9s
+   113/401 | loss=1.2963 ev=0.414 agents=88 avg_r=4.9068 sum_r=1256.15 x<0=0.01 elig=0.63 dorfler_tail=0.07 floor=0 sel=30 8.0s
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+   115/401 | loss=1.0023 ev=0.462 agents=1043 avg_r=4.6932 sum_r=1201.45 x<0=0.01 elig=0.64 dorfler_tail=0.07 floor=0 sel=29 7.7s
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+   140/401 | loss=0.8756 ev=0.491 agents=34 avg_r=4.0575 sum_r=1038.73 x<0=0.00 elig=0.64 dorfler_tail=0.07 floor=0 sel=26 7.8s
+   141/401 | loss=1.0863 ev=0.455 agents=202 avg_r=4.4626 sum_r=1142.43 x<0=0.00 elig=0.64 dorfler_tail=0.07 floor=0 sel=28 8.2s
+   142/401 | loss=0.8633 ev=0.492 agents=599 avg_r=3.6977 sum_r=946.60 x<0=0.00 elig=0.63 dorfler_tail=0.07 floor=0 sel=27 7.7s
+   143/401 | loss=1.2714 ev=0.450 agents=83 avg_r=3.4606 sum_r=885.91 x<0=0.00 elig=0.63 dorfler_tail=0.07 floor=0 sel=27 7.8s
+   144/401 | loss=0.8689 ev=0.480 agents=212 avg_r=5.9020 sum_r=1510.92 x<0=0.00 elig=0.64 dorfler_tail=0.07 floor=0 sel=31 8.2s
+   145/401 | loss=0.8527 ev=0.457 agents=466 avg_r=3.3779 sum_r=864.73 x<0=0.00 elig=0.64 dorfler_tail=0.07 floor=0 sel=28 7.7s
+   146/401 | loss=1.0791 ev=0.436 agents=41 avg_r=3.9742 sum_r=1017.40 x<0=0.00 elig=0.64 dorfler_tail=0.07 floor=0 sel=27 7.6s
+   147/401 | loss=1.0243 ev=0.483 agents=201 avg_r=4.0608 sum_r=1039.56 x<0=0.00 elig=0.64 dorfler_tail=0.07 floor=0 sel=27 7.7s
+   148/401 | loss=0.8642 ev=0.439 agents=169 avg_r=5.0525 sum_r=1293.44 x<0=0.00 elig=0.64 dorfler_tail=0.07 floor=0 sel=29 7.9s
+   149/401 | loss=1.2060 ev=0.492 agents=1118 avg_r=3.4406 sum_r=880.81 x<0=0.00 elig=0.64 dorfler_tail=0.07 floor=0 sel=28 7.8s
+   150/401 | loss=0.8956 ev=0.491 agents=139 avg_r=4.4020 sum_r=1126.90 x<0=0.00 elig=0.63 dorfler_tail=0.07 floor=0 sel=28 7.7s
+[Checkpoint] saved → checkpoints/model_iter0150.pt
+   151/401 | loss=0.8862 ev=0.439 agents=36 avg_r=3.6186 sum_r=926.35 x<0=0.00 elig=0.64 dorfler_tail=0.07 floor=0 sel=26 7.4s
+   152/401 | loss=1.1976 ev=0.436 agents=374 avg_r=5.2749 sum_r=1350.39 x<0=0.00 elig=0.64 dorfler_tail=0.07 floor=0 sel=30 8.0s
+   153/401 | loss=0.7750 ev=0.453 agents=203 avg_r=3.3719 sum_r=863.21 x<0=0.00 elig=0.64 dorfler_tail=0.07 floor=0 sel=26 7.5s
+   154/401 | loss=1.1222 ev=0.448 agents=498 avg_r=5.2013 sum_r=1331.52 x<0=0.00 elig=0.64 dorfler_tail=0.07 floor=0 sel=29 7.8s
+   155/401 | loss=0.8401 ev=0.498 agents=174 avg_r=4.3179 sum_r=1105.39 x<0=0.00 elig=0.64 dorfler_tail=0.07 floor=0 sel=27 7.5s
+   156/401 | loss=1.1951 ev=0.475 agents=144 avg_r=4.7607 sum_r=1218.73 x<0=0.00 elig=0.64 dorfler_tail=0.07 floor=0 sel=29 7.9s
+   157/401 | loss=1.0364 ev=0.488 agents=233 avg_r=4.6508 sum_r=1190.61 x<0=0.00 elig=0.64 dorfler_tail=0.07 floor=0 sel=29 7.9s
+   158/401 | loss=1.1938 ev=0.437 agents=40 avg_r=4.8137 sum_r=1232.31 x<0=0.00 elig=0.65 dorfler_tail=0.07 floor=0 sel=28 7.7s
+   159/401 | loss=0.7339 ev=0.442 agents=401 avg_r=2.6907 sum_r=688.82 x<0=0.00 elig=0.64 dorfler_tail=0.06 floor=0 sel=27 7.5s
+   160/401 | loss=0.9124 ev=0.494 agents=377 avg_r=5.1447 sum_r=1317.04 x<0=0.00 elig=0.65 dorfler_tail=0.07 floor=0 sel=27 7.7s
+   161/401 | loss=1.1279 ev=0.482 agents=34 avg_r=5.6036 sum_r=1434.53 x<0=0.00 elig=0.64 dorfler_tail=0.07 floor=0 sel=30 8.0s
+   162/401 | loss=0.9648 ev=0.472 agents=725 avg_r=4.8624 sum_r=1244.77 x<0=0.00 elig=0.65 dorfler_tail=0.07 floor=0 sel=29 7.8s
+   163/401 | loss=0.8031 ev=0.507 agents=276 avg_r=2.6097 sum_r=668.09 x<0=0.00 elig=0.64 dorfler_tail=0.06 floor=0 sel=23 7.6s
+   164/401 | loss=1.3767 ev=0.402 agents=177 avg_r=5.0539 sum_r=1293.81 x<0=0.00 elig=0.64 dorfler_tail=0.07 floor=0 sel=31 8.4s
+   165/401 | loss=0.9780 ev=0.513 agents=158 avg_r=4.9213 sum_r=1259.84 x<0=0.00 elig=0.64 dorfler_tail=0.07 floor=0 sel=29 8.0s
+   166/401 | loss=0.9135 ev=0.480 agents=397 avg_r=3.7623 sum_r=963.14 x<0=0.00 elig=0.65 dorfler_tail=0.07 floor=0 sel=27 7.8s
+   167/401 | loss=1.1074 ev=0.503 agents=193 avg_r=5.2436 sum_r=1342.35 x<0=0.00 elig=0.64 dorfler_tail=0.07 floor=0 sel=30 8.0s
+   168/401 | loss=1.1870 ev=0.476 agents=1235 avg_r=3.8139 sum_r=976.35 x<0=0.00 elig=0.65 dorfler_tail=0.07 floor=0 sel=27 7.6s
+   169/401 | loss=1.2314 ev=0.459 agents=476 avg_r=2.9524 sum_r=755.82 x<0=0.00 elig=0.65 dorfler_tail=0.07 floor=0 sel=29 7.9s
+slurmstepd: error: *** JOB 4533 ON node06 CANCELLED AT 2026-05-29T14:58:13 ***
diff --git a/logs/train_4534.out b/logs/train_4534.out
new file mode 100644
index 0000000..cf2e4b7
--- /dev/null
+++ b/logs/train_4534.out
@@ -0,0 +1,418 @@
+Starting training at Fri 29 May 14:58:18 CST 2026
+Running on node: node06
+[Device] cuda
+[Env] node_feats=14 edge_feats=1 act_dim=1
+[Model] params=92,804
+     1/401 | loss=1.4128 ev=-0.004 agents=109 avg_r=-2.9617 sum_r=-758.20 x<0=0.69 elig=0.58 dorfler_tail=0.09 floor=0 sel=35 8.6s
+     2/401 | loss=1.3206 ev=0.021 agents=193 avg_r=-0.3258 sum_r=-83.41 x<0=0.62 elig=0.58 dorfler_tail=0.08 floor=0 sel=32 7.8s
+     3/401 | loss=1.2607 ev=0.053 agents=39 avg_r=-3.3286 sum_r=-852.13 x<0=0.56 elig=0.59 dorfler_tail=0.08 floor=0 sel=32 7.7s
+     4/401 | loss=1.3325 ev=0.075 agents=34 avg_r=0.7804 sum_r=199.78 x<0=0.52 elig=0.58 dorfler_tail=0.09 floor=0 sel=35 8.2s
+     5/401 | loss=1.2579 ev=0.094 agents=88 avg_r=-3.0086 sum_r=-770.19 x<0=0.43 elig=0.59 dorfler_tail=0.08 floor=0 sel=32 8.0s
+     6/401 | loss=1.2490 ev=0.117 agents=36 avg_r=-0.7408 sum_r=-189.63 x<0=0.40 elig=0.59 dorfler_tail=0.08 floor=0 sel=32 7.7s
+     7/401 | loss=1.1303 ev=0.172 agents=34 avg_r=-0.5650 sum_r=-144.65 x<0=0.35 elig=0.58 dorfler_tail=0.08 floor=0 sel=35 8.0s
+     8/401 | loss=1.1519 ev=0.223 agents=133 avg_r=-0.3562 sum_r=-91.18 x<0=0.29 elig=0.59 dorfler_tail=0.08 floor=0 sel=33 7.8s
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+    16/401 | loss=1.0478 ev=0.353 agents=34 avg_r=-1.6244 sum_r=-415.85 x<0=0.21 elig=0.59 dorfler_tail=0.08 floor=0 sel=29 7.4s
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+    18/401 | loss=0.9338 ev=0.365 agents=34 avg_r=0.5794 sum_r=148.32 x<0=0.30 elig=0.58 dorfler_tail=0.08 floor=0 sel=32 7.7s
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+    26/401 | loss=0.8252 ev=0.385 agents=34 avg_r=-0.2623 sum_r=-67.15 x<0=0.12 elig=0.58 dorfler_tail=0.08 floor=0 sel=34 7.8s
+    27/401 | loss=0.8039 ev=0.408 agents=176 avg_r=0.3361 sum_r=86.04 x<0=0.11 elig=0.59 dorfler_tail=0.08 floor=0 sel=31 7.9s
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+    32/401 | loss=0.8750 ev=0.418 agents=34 avg_r=0.3083 sum_r=78.94 x<0=0.06 elig=0.59 dorfler_tail=0.08 floor=0 sel=33 7.7s
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+    34/401 | loss=0.8724 ev=0.418 agents=132 avg_r=0.1713 sum_r=43.85 x<0=0.06 elig=0.59 dorfler_tail=0.07 floor=0 sel=31 7.5s
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+    37/401 | loss=0.9037 ev=0.426 agents=228 avg_r=0.5137 sum_r=131.52 x<0=0.04 elig=0.59 dorfler_tail=0.08 floor=0 sel=31 7.5s
+    38/401 | loss=0.9280 ev=0.353 agents=34 avg_r=1.7908 sum_r=458.45 x<0=0.05 elig=0.59 dorfler_tail=0.07 floor=0 sel=31 7.5s
+    39/401 | loss=0.7340 ev=0.438 agents=194 avg_r=1.8975 sum_r=485.76 x<0=0.05 elig=0.59 dorfler_tail=0.08 floor=0 sel=31 7.4s
+    40/401 | loss=0.8670 ev=0.364 agents=228 avg_r=2.4297 sum_r=621.99 x<0=0.07 elig=0.59 dorfler_tail=0.08 floor=0 sel=33 7.7s
+    41/401 | loss=0.8306 ev=0.403 agents=199 avg_r=1.3996 sum_r=358.30 x<0=0.06 elig=0.59 dorfler_tail=0.07 floor=0 sel=29 7.3s
+    42/401 | loss=0.7935 ev=0.456 agents=40 avg_r=2.2913 sum_r=586.59 x<0=0.06 elig=0.59 dorfler_tail=0.07 floor=0 sel=31 7.5s
+    43/401 | loss=0.7569 ev=0.425 agents=34 avg_r=1.5674 sum_r=401.25 x<0=0.05 elig=0.59 dorfler_tail=0.08 floor=0 sel=31 7.5s
+    44/401 | loss=0.8324 ev=0.425 agents=193 avg_r=1.5056 sum_r=385.44 x<0=0.07 elig=0.59 dorfler_tail=0.08 floor=0 sel=32 7.5s
+    45/401 | loss=0.8032 ev=0.458 agents=230 avg_r=1.1388 sum_r=291.54 x<0=0.06 elig=0.59 dorfler_tail=0.07 floor=0 sel=29 7.3s
+    46/401 | loss=0.8043 ev=0.436 agents=34 avg_r=2.3922 sum_r=612.39 x<0=0.07 elig=0.59 dorfler_tail=0.08 floor=0 sel=31 7.5s
+    47/401 | loss=0.7410 ev=0.443 agents=120 avg_r=3.2861 sum_r=841.24 x<0=0.08 elig=0.59 dorfler_tail=0.08 floor=0 sel=31 7.4s
+    48/401 | loss=0.8324 ev=0.403 agents=34 avg_r=0.2820 sum_r=72.19 x<0=0.05 elig=0.59 dorfler_tail=0.08 floor=0 sel=31 7.5s
+    49/401 | loss=0.7722 ev=0.461 agents=118 avg_r=3.1596 sum_r=808.87 x<0=0.06 elig=0.59 dorfler_tail=0.08 floor=0 sel=32 8.0s
+    50/401 | loss=0.7615 ev=0.445 agents=203 avg_r=1.2732 sum_r=325.95 x<0=0.03 elig=0.59 dorfler_tail=0.07 floor=0 sel=30 7.7s
+[Checkpoint] saved → checkpoints/model_iter0050.pt
+    51/401 | loss=0.7829 ev=0.428 agents=1574 avg_r=1.8165 sum_r=465.03 x<0=0.02 elig=0.59 dorfler_tail=0.08 floor=0 sel=31 7.7s
+    52/401 | loss=0.7954 ev=0.432 agents=278 avg_r=2.1507 sum_r=550.57 x<0=0.02 elig=0.59 dorfler_tail=0.08 floor=0 sel=31 7.5s
+    53/401 | loss=0.6962 ev=0.449 agents=133 avg_r=2.0534 sum_r=525.66 x<0=0.02 elig=0.59 dorfler_tail=0.07 floor=0 sel=29 7.4s
+    54/401 | loss=0.7625 ev=0.454 agents=231 avg_r=1.5343 sum_r=392.79 x<0=0.02 elig=0.59 dorfler_tail=0.08 floor=0 sel=31 7.5s
+    55/401 | loss=0.7736 ev=0.414 agents=97 avg_r=1.6580 sum_r=424.46 x<0=0.02 elig=0.59 dorfler_tail=0.08 floor=0 sel=32 7.6s
+    56/401 | loss=0.8158 ev=0.454 agents=108 avg_r=1.4593 sum_r=373.59 x<0=0.03 elig=0.60 dorfler_tail=0.07 floor=0 sel=28 7.3s
+    57/401 | loss=0.8160 ev=0.384 agents=140 avg_r=1.2522 sum_r=320.57 x<0=0.04 elig=0.59 dorfler_tail=0.08 floor=0 sel=31 7.5s
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+    60/401 | loss=0.7958 ev=0.444 agents=64 avg_r=0.6857 sum_r=175.55 x<0=0.02 elig=0.59 dorfler_tail=0.08 floor=0 sel=31 7.5s
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+    76/401 | loss=0.8142 ev=0.417 agents=728 avg_r=3.7060 sum_r=948.74 x<0=0.04 elig=0.60 dorfler_tail=0.07 floor=0 sel=31 7.6s
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+    91/401 | loss=1.0702 ev=0.415 agents=103 avg_r=2.9575 sum_r=757.12 x<0=0.11 elig=0.62 dorfler_tail=0.08 floor=0 sel=29 7.8s
+    92/401 | loss=1.0768 ev=0.393 agents=222 avg_r=2.3631 sum_r=604.95 x<0=0.09 elig=0.62 dorfler_tail=0.07 floor=0 sel=28 7.6s
+    93/401 | loss=0.8536 ev=0.446 agents=817 avg_r=2.8966 sum_r=741.53 x<0=0.10 elig=0.62 dorfler_tail=0.07 floor=0 sel=28 7.5s
+    94/401 | loss=1.0326 ev=0.381 agents=263 avg_r=3.2866 sum_r=841.36 x<0=0.11 elig=0.62 dorfler_tail=0.07 floor=0 sel=28 7.9s
+    95/401 | loss=0.9661 ev=0.438 agents=457 avg_r=4.7830 sum_r=1224.46 x<0=0.14 elig=0.62 dorfler_tail=0.08 floor=0 sel=32 8.7s
+    96/401 | loss=1.0307 ev=0.410 agents=146 avg_r=1.6996 sum_r=435.09 x<0=0.12 elig=0.62 dorfler_tail=0.07 floor=0 sel=28 7.6s
+    97/401 | loss=1.0506 ev=0.374 agents=1822 avg_r=4.6356 sum_r=1186.73 x<0=0.13 elig=0.62 dorfler_tail=0.07 floor=0 sel=28 8.0s
+    98/401 | loss=1.0002 ev=0.431 agents=247 avg_r=3.5428 sum_r=906.95 x<0=0.13 elig=0.63 dorfler_tail=0.07 floor=0 sel=27 7.6s
+    99/401 | loss=0.9919 ev=0.429 agents=438 avg_r=2.5796 sum_r=660.39 x<0=0.15 elig=0.63 dorfler_tail=0.07 floor=0 sel=28 7.7s
+   100/401 | loss=1.1839 ev=0.424 agents=80 avg_r=2.8253 sum_r=723.27 x<0=0.12 elig=0.62 dorfler_tail=0.07 floor=0 sel=29 7.7s
+[Checkpoint] saved → checkpoints/model_iter0100.pt
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+   105/401 | loss=1.0714 ev=0.429 agents=375 avg_r=2.9595 sum_r=757.64 x<0=0.14 elig=0.62 dorfler_tail=0.07 floor=0 sel=29 7.6s
+   106/401 | loss=1.0984 ev=0.407 agents=34 avg_r=4.7091 sum_r=1205.54 x<0=0.16 elig=0.63 dorfler_tail=0.07 floor=0 sel=29 7.7s
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+   108/401 | loss=1.0474 ev=0.424 agents=92 avg_r=3.6964 sum_r=946.27 x<0=0.14 elig=0.63 dorfler_tail=0.07 floor=0 sel=26 7.4s
+   109/401 | loss=1.0957 ev=0.424 agents=225 avg_r=4.3635 sum_r=1117.06 x<0=0.15 elig=0.62 dorfler_tail=0.07 floor=0 sel=30 7.9s
+   110/401 | loss=1.0859 ev=0.396 agents=182 avg_r=2.8480 sum_r=729.08 x<0=0.15 elig=0.63 dorfler_tail=0.07 floor=0 sel=29 7.6s
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+   112/401 | loss=1.0549 ev=0.444 agents=175 avg_r=4.9807 sum_r=1275.05 x<0=0.15 elig=0.63 dorfler_tail=0.07 floor=0 sel=30 7.8s
+   113/401 | loss=1.0457 ev=0.431 agents=132 avg_r=4.3526 sum_r=1114.27 x<0=0.13 elig=0.63 dorfler_tail=0.07 floor=0 sel=31 8.0s
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+[Checkpoint] saved → checkpoints/model_iter0150.pt
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+[Checkpoint] saved → checkpoints/model_iter0200.pt
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+[Checkpoint] saved → checkpoints/model_iter0250.pt
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+[Checkpoint] saved → checkpoints/model_iter0300.pt
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+   343/401 | loss=0.7043 ev=0.532 agents=44 avg_r=1.0479 sum_r=268.27 x<0=0.14 elig=0.59 dorfler_tail=0.08 floor=0 sel=31 7.4s
+   344/401 | loss=0.6269 ev=0.553 agents=308 avg_r=1.5500 sum_r=396.81 x<0=0.15 elig=0.59 dorfler_tail=0.08 floor=0 sel=30 7.3s
+   345/401 | loss=0.5842 ev=0.580 agents=704 avg_r=2.1546 sum_r=551.57 x<0=0.12 elig=0.59 dorfler_tail=0.08 floor=0 sel=29 7.6s
+   346/401 | loss=0.6299 ev=0.570 agents=41 avg_r=0.7011 sum_r=179.49 x<0=0.16 elig=0.59 dorfler_tail=0.08 floor=0 sel=33 8.0s
+   347/401 | loss=0.6316 ev=0.571 agents=278 avg_r=1.6173 sum_r=414.03 x<0=0.15 elig=0.59 dorfler_tail=0.08 floor=0 sel=28 7.3s
+   348/401 | loss=0.6115 ev=0.573 agents=34 avg_r=0.1809 sum_r=46.32 x<0=0.17 elig=0.59 dorfler_tail=0.08 floor=0 sel=29 7.4s
+   349/401 | loss=0.6532 ev=0.557 agents=242 avg_r=0.8962 sum_r=229.43 x<0=0.12 elig=0.59 dorfler_tail=0.08 floor=0 sel=31 7.5s
+   350/401 | loss=0.6516 ev=0.582 agents=44 avg_r=1.0303 sum_r=263.76 x<0=0.15 elig=0.59 dorfler_tail=0.08 floor=0 sel=31 7.6s
+[Checkpoint] saved → checkpoints/model_iter0350.pt
+   351/401 | loss=0.6227 ev=0.554 agents=201 avg_r=0.7558 sum_r=193.50 x<0=0.15 elig=0.59 dorfler_tail=0.08 floor=0 sel=30 7.3s
+   352/401 | loss=0.5750 ev=0.605 agents=34 avg_r=0.5050 sum_r=129.29 x<0=0.14 elig=0.58 dorfler_tail=0.08 floor=0 sel=30 7.4s
+   353/401 | loss=0.6413 ev=0.544 agents=457 avg_r=0.2005 sum_r=51.32 x<0=0.17 elig=0.60 dorfler_tail=0.07 floor=0 sel=26 6.9s
+   354/401 | loss=0.6211 ev=0.589 agents=120 avg_r=2.0601 sum_r=527.38 x<0=0.12 elig=0.59 dorfler_tail=0.08 floor=0 sel=33 7.6s
+   355/401 | loss=0.6174 ev=0.574 agents=34 avg_r=1.1792 sum_r=301.88 x<0=0.15 elig=0.59 dorfler_tail=0.08 floor=0 sel=30 7.3s
+   356/401 | loss=0.6271 ev=0.563 agents=267 avg_r=0.9035 sum_r=231.30 x<0=0.15 elig=0.59 dorfler_tail=0.08 floor=0 sel=31 7.4s
+   357/401 | loss=0.6969 ev=0.569 agents=34 avg_r=-0.5932 sum_r=-151.87 x<0=0.14 elig=0.59 dorfler_tail=0.08 floor=0 sel=31 7.4s
+   358/401 | loss=0.6315 ev=0.543 agents=34 avg_r=0.1535 sum_r=39.30 x<0=0.15 elig=0.59 dorfler_tail=0.08 floor=0 sel=31 7.4s
+   359/401 | loss=0.5787 ev=0.598 agents=64 avg_r=-0.8402 sum_r=-215.10 x<0=0.10 elig=0.59 dorfler_tail=0.08 floor=0 sel=30 7.3s
+   360/401 | loss=0.6417 ev=0.555 agents=174 avg_r=0.4168 sum_r=106.70 x<0=0.19 elig=0.59 dorfler_tail=0.08 floor=0 sel=31 7.4s
+   361/401 | loss=0.6239 ev=0.563 agents=210 avg_r=0.3188 sum_r=81.61 x<0=0.13 elig=0.59 dorfler_tail=0.08 floor=0 sel=29 7.2s
+   362/401 | loss=0.5985 ev=0.578 agents=1136 avg_r=0.0481 sum_r=12.32 x<0=0.15 elig=0.59 dorfler_tail=0.08 floor=0 sel=30 7.3s
+   363/401 | loss=0.5902 ev=0.569 agents=34 avg_r=-0.3036 sum_r=-77.73 x<0=0.15 elig=0.59 dorfler_tail=0.08 floor=0 sel=31 7.4s
+   364/401 | loss=0.6606 ev=0.567 agents=147 avg_r=-1.4026 sum_r=-359.07 x<0=0.14 elig=0.59 dorfler_tail=0.08 floor=0 sel=30 7.3s
+   365/401 | loss=0.6312 ev=0.553 agents=150 avg_r=0.4739 sum_r=121.33 x<0=0.13 elig=0.59 dorfler_tail=0.08 floor=0 sel=32 7.6s
+   366/401 | loss=0.6945 ev=0.551 agents=219 avg_r=-1.1566 sum_r=-296.08 x<0=0.14 elig=0.59 dorfler_tail=0.07 floor=0 sel=27 7.0s
+   367/401 | loss=0.5808 ev=0.596 agents=85 avg_r=1.6020 sum_r=410.10 x<0=0.13 elig=0.58 dorfler_tail=0.09 floor=0 sel=32 7.7s
+   368/401 | loss=0.6056 ev=0.568 agents=762 avg_r=-1.3623 sum_r=-348.74 x<0=0.12 elig=0.59 dorfler_tail=0.08 floor=0 sel=30 7.7s
+   369/401 | loss=0.6481 ev=0.558 agents=177 avg_r=-0.9408 sum_r=-240.85 x<0=0.17 elig=0.59 dorfler_tail=0.08 floor=0 sel=31 7.7s
+   370/401 | loss=0.6171 ev=0.589 agents=1015 avg_r=-0.9711 sum_r=-248.60 x<0=0.14 elig=0.59 dorfler_tail=0.08 floor=0 sel=30 7.5s
+   371/401 | loss=0.6382 ev=0.581 agents=97 avg_r=-0.9976 sum_r=-255.40 x<0=0.15 elig=0.59 dorfler_tail=0.08 floor=0 sel=30 7.5s
+   372/401 | loss=0.6350 ev=0.563 agents=553 avg_r=-2.2484 sum_r=-575.58 x<0=0.14 elig=0.59 dorfler_tail=0.08 floor=0 sel=31 7.5s
+   373/401 | loss=0.6417 ev=0.550 agents=83 avg_r=-1.2092 sum_r=-309.56 x<0=0.17 elig=0.59 dorfler_tail=0.09 floor=0 sel=30 7.4s
+   374/401 | loss=0.5959 ev=0.596 agents=72 avg_r=-2.0364 sum_r=-521.32 x<0=0.13 elig=0.58 dorfler_tail=0.09 floor=0 sel=34 7.8s
+   375/401 | loss=0.5694 ev=0.598 agents=154 avg_r=-0.1396 sum_r=-35.75 x<0=0.17 elig=0.59 dorfler_tail=0.08 floor=0 sel=28 7.3s
+   376/401 | loss=0.6582 ev=0.562 agents=141 avg_r=-3.1031 sum_r=-794.39 x<0=0.17 elig=0.59 dorfler_tail=0.08 floor=0 sel=30 7.4s
+   377/401 | loss=0.5972 ev=0.597 agents=1262 avg_r=-1.6131 sum_r=-412.95 x<0=0.15 elig=0.58 dorfler_tail=0.09 floor=0 sel=31 7.5s
+   378/401 | loss=0.6511 ev=0.595 agents=509 avg_r=-3.4710 sum_r=-888.58 x<0=0.18 elig=0.59 dorfler_tail=0.08 floor=0 sel=30 7.3s
+   379/401 | loss=0.6209 ev=0.573 agents=36 avg_r=-2.1022 sum_r=-538.17 x<0=0.14 elig=0.59 dorfler_tail=0.08 floor=0 sel=32 7.6s
+   380/401 | loss=0.5629 ev=0.624 agents=600 avg_r=-1.5907 sum_r=-407.23 x<0=0.14 elig=0.58 dorfler_tail=0.09 floor=0 sel=30 7.4s
+   381/401 | loss=0.6222 ev=0.572 agents=200 avg_r=-1.0094 sum_r=-258.41 x<0=0.13 elig=0.59 dorfler_tail=0.08 floor=0 sel=31 7.4s
+   382/401 | loss=0.6545 ev=0.550 agents=388 avg_r=-3.5082 sum_r=-898.10 x<0=0.23 elig=0.60 dorfler_tail=0.08 floor=0 sel=28 7.2s
+   383/401 | loss=0.5294 ev=0.636 agents=85 avg_r=-0.4136 sum_r=-105.88 x<0=0.12 elig=0.58 dorfler_tail=0.09 floor=0 sel=32 7.5s
+   384/401 | loss=0.5944 ev=0.579 agents=453 avg_r=-2.0541 sum_r=-525.84 x<0=0.18 elig=0.59 dorfler_tail=0.08 floor=0 sel=30 7.4s
+   385/401 | loss=0.6282 ev=0.578 agents=171 avg_r=-1.6239 sum_r=-415.72 x<0=0.17 elig=0.59 dorfler_tail=0.08 floor=0 sel=30 7.3s
+   386/401 | loss=0.6290 ev=0.570 agents=561 avg_r=-1.0137 sum_r=-259.51 x<0=0.15 elig=0.59 dorfler_tail=0.08 floor=0 sel=30 7.4s
+   387/401 | loss=0.5582 ev=0.611 agents=404 avg_r=-0.5416 sum_r=-138.65 x<0=0.14 elig=0.59 dorfler_tail=0.09 floor=0 sel=31 7.4s
+   388/401 | loss=0.5969 ev=0.559 agents=154 avg_r=-5.0462 sum_r=-1291.82 x<0=0.17 elig=0.59 dorfler_tail=0.08 floor=0 sel=28 7.2s
+   389/401 | loss=0.6544 ev=0.548 agents=278 avg_r=-1.2462 sum_r=-319.03 x<0=0.18 elig=0.59 dorfler_tail=0.08 floor=0 sel=31 7.4s
+   390/401 | loss=0.6538 ev=0.587 agents=856 avg_r=-1.0032 sum_r=-256.82 x<0=0.17 elig=0.58 dorfler_tail=0.08 floor=0 sel=31 7.9s
+   391/401 | loss=0.5737 ev=0.593 agents=101 avg_r=-2.4208 sum_r=-619.72 x<0=0.15 elig=0.58 dorfler_tail=0.08 floor=0 sel=31 8.0s
+   392/401 | loss=0.5898 ev=0.601 agents=101 avg_r=-1.4010 sum_r=-358.67 x<0=0.19 elig=0.59 dorfler_tail=0.08 floor=0 sel=29 7.5s
+   393/401 | loss=0.5977 ev=0.587 agents=219 avg_r=-2.3206 sum_r=-594.07 x<0=0.11 elig=0.58 dorfler_tail=0.09 floor=0 sel=31 7.7s
+   394/401 | loss=0.5978 ev=0.583 agents=832 avg_r=-2.7761 sum_r=-710.69 x<0=0.19 elig=0.59 dorfler_tail=0.08 floor=0 sel=32 7.8s
+   395/401 | loss=0.5630 ev=0.607 agents=118 avg_r=-2.8482 sum_r=-729.14 x<0=0.15 elig=0.58 dorfler_tail=0.08 floor=0 sel=30 7.5s
+   396/401 | loss=0.6266 ev=0.557 agents=980 avg_r=-1.5726 sum_r=-402.60 x<0=0.20 elig=0.58 dorfler_tail=0.08 floor=0 sel=30 7.4s
+   397/401 | loss=0.5852 ev=0.599 agents=55 avg_r=-4.5732 sum_r=-1170.75 x<0=0.18 elig=0.59 dorfler_tail=0.08 floor=0 sel=31 7.5s
+   398/401 | loss=0.6173 ev=0.583 agents=604 avg_r=-1.0687 sum_r=-273.59 x<0=0.16 elig=0.58 dorfler_tail=0.09 floor=0 sel=30 7.4s
+   399/401 | loss=0.5544 ev=0.622 agents=278 avg_r=-2.7659 sum_r=-708.06 x<0=0.18 elig=0.58 dorfler_tail=0.08 floor=0 sel=30 7.4s
+   400/401 | loss=0.6305 ev=0.572 agents=400 avg_r=-2.0476 sum_r=-524.18 x<0=0.20 elig=0.59 dorfler_tail=0.08 floor=0 sel=30 7.4s
+[Checkpoint] saved → checkpoints/model_iter0400.pt
+   401/401 | loss=0.6506 ev=0.589 agents=230 avg_r=0.0894 sum_r=22.90 x<0=0.13 elig=0.59 dorfler_tail=0.08 floor=0 sel=31 7.4s
+[Checkpoint] saved → checkpoints/model_iter0401.pt
+[Checkpoint] saved → checkpoints/model_final.pt
+[Train] done, total time 3065.4s
+Training finished at Fri 29 May 15:49:40 CST 2026
diff --git a/logs/train_4537.out b/logs/train_4537.out
new file mode 100644
index 0000000..49b1008
--- /dev/null
+++ b/logs/train_4537.out
@@ -0,0 +1,418 @@
+Starting training at Sat 30 May 15:16:09 CST 2026
+Running on node: node06
+[Device] cuda
+[Env] node_feats=13 edge_feats=1 act_dim=1
+[Model] params=92,740
+     1/401 | loss=1.4016 ev=-0.007 agents=109 avg_r=-3.9659 sum_r=-1015.28 x<0=0.79 elig=0.58 dorfler_tail=0.09 floor=0 sel=35 8.7s
+     2/401 | loss=1.2826 ev=0.030 agents=193 avg_r=-2.0419 sum_r=-522.72 x<0=0.80 elig=0.58 dorfler_tail=0.08 floor=0 sel=32 7.9s
+     3/401 | loss=1.2362 ev=0.058 agents=39 avg_r=-4.8186 sum_r=-1233.57 x<0=0.80 elig=0.59 dorfler_tail=0.08 floor=0 sel=32 7.8s
+     4/401 | loss=1.2801 ev=0.101 agents=34 avg_r=-0.7326 sum_r=-187.54 x<0=0.77 elig=0.58 dorfler_tail=0.09 floor=0 sel=35 8.3s
+     5/401 | loss=1.1594 ev=0.132 agents=88 avg_r=-3.2420 sum_r=-829.95 x<0=0.74 elig=0.59 dorfler_tail=0.08 floor=0 sel=32 8.0s
+     6/401 | loss=1.1517 ev=0.181 agents=36 avg_r=-1.5350 sum_r=-392.96 x<0=0.70 elig=0.59 dorfler_tail=0.08 floor=0 sel=32 7.9s
+     7/401 | loss=1.0153 ev=0.253 agents=34 avg_r=-0.7087 sum_r=-181.42 x<0=0.67 elig=0.58 dorfler_tail=0.08 floor=0 sel=35 8.1s
+     8/401 | loss=1.0623 ev=0.283 agents=133 avg_r=-0.8781 sum_r=-224.79 x<0=0.65 elig=0.59 dorfler_tail=0.08 floor=0 sel=33 7.9s
+     9/401 | loss=0.9819 ev=0.304 agents=79 avg_r=-0.5083 sum_r=-130.11 x<0=0.61 elig=0.59 dorfler_tail=0.08 floor=0 sel=31 7.7s
+    10/401 | loss=0.9743 ev=0.299 agents=82 avg_r=-2.3678 sum_r=-606.16 x<0=0.59 elig=0.59 dorfler_tail=0.08 floor=0 sel=33 7.9s
+    11/401 | loss=1.0183 ev=0.320 agents=60 avg_r=1.3849 sum_r=354.54 x<0=0.53 elig=0.59 dorfler_tail=0.08 floor=0 sel=31 7.6s
+    12/401 | loss=0.9395 ev=0.343 agents=48 avg_r=0.4274 sum_r=109.42 x<0=0.50 elig=0.59 dorfler_tail=0.08 floor=0 sel=33 7.8s
+    13/401 | loss=0.8380 ev=0.367 agents=88 avg_r=-0.3599 sum_r=-92.14 x<0=0.45 elig=0.59 dorfler_tail=0.08 floor=0 sel=32 7.8s
+    14/401 | loss=0.9338 ev=0.341 agents=40 avg_r=0.1794 sum_r=45.93 x<0=0.42 elig=0.59 dorfler_tail=0.08 floor=0 sel=32 7.7s
+    15/401 | loss=0.8502 ev=0.381 agents=101 avg_r=0.1944 sum_r=49.77 x<0=0.42 elig=0.59 dorfler_tail=0.08 floor=0 sel=33 8.0s
+    16/401 | loss=0.9830 ev=0.370 agents=34 avg_r=-1.4113 sum_r=-361.30 x<0=0.40 elig=0.59 dorfler_tail=0.08 floor=0 sel=29 7.4s
+    17/401 | loss=0.8119 ev=0.428 agents=132 avg_r=1.8346 sum_r=469.66 x<0=0.42 elig=0.59 dorfler_tail=0.08 floor=0 sel=33 7.8s
+    18/401 | loss=0.8296 ev=0.394 agents=34 avg_r=-0.0265 sum_r=-6.80 x<0=0.36 elig=0.59 dorfler_tail=0.08 floor=0 sel=32 7.7s
+    19/401 | loss=0.8208 ev=0.414 agents=201 avg_r=-0.1825 sum_r=-46.71 x<0=0.34 elig=0.59 dorfler_tail=0.08 floor=0 sel=34 7.9s
+    20/401 | loss=0.8558 ev=0.396 agents=120 avg_r=0.8307 sum_r=212.65 x<0=0.30 elig=0.59 dorfler_tail=0.08 floor=0 sel=31 7.7s
+    21/401 | loss=0.8402 ev=0.410 agents=78 avg_r=-0.2640 sum_r=-67.58 x<0=0.33 elig=0.59 dorfler_tail=0.08 floor=0 sel=31 7.7s
+    22/401 | loss=0.8100 ev=0.413 agents=44 avg_r=0.1745 sum_r=44.68 x<0=0.33 elig=0.59 dorfler_tail=0.08 floor=0 sel=32 7.7s
+    23/401 | loss=0.7978 ev=0.416 agents=36 avg_r=-0.3726 sum_r=-95.38 x<0=0.27 elig=0.59 dorfler_tail=0.08 floor=0 sel=32 7.7s
+    24/401 | loss=0.7886 ev=0.456 agents=175 avg_r=2.2911 sum_r=586.53 x<0=0.23 elig=0.59 dorfler_tail=0.08 floor=0 sel=33 7.9s
+    25/401 | loss=0.8188 ev=0.402 agents=34 avg_r=0.0163 sum_r=4.18 x<0=0.24 elig=0.59 dorfler_tail=0.07 floor=0 sel=28 7.4s
+    26/401 | loss=0.8580 ev=0.417 agents=34 avg_r=-0.2140 sum_r=-54.78 x<0=0.23 elig=0.59 dorfler_tail=0.08 floor=0 sel=33 7.9s
+    27/401 | loss=0.7731 ev=0.413 agents=176 avg_r=-0.0139 sum_r=-3.56 x<0=0.22 elig=0.59 dorfler_tail=0.07 floor=0 sel=31 8.0s
+    28/401 | loss=0.8363 ev=0.407 agents=219 avg_r=-0.2731 sum_r=-69.90 x<0=0.21 elig=0.59 dorfler_tail=0.08 floor=0 sel=32 8.3s
+    29/401 | loss=0.8037 ev=0.407 agents=44 avg_r=1.4718 sum_r=376.77 x<0=0.22 elig=0.59 dorfler_tail=0.08 floor=0 sel=32 8.0s
+    30/401 | loss=0.7398 ev=0.460 agents=133 avg_r=1.9308 sum_r=494.30 x<0=0.21 elig=0.59 dorfler_tail=0.08 floor=0 sel=29 7.6s
+    31/401 | loss=0.8308 ev=0.421 agents=44 avg_r=1.0891 sum_r=278.82 x<0=0.19 elig=0.59 dorfler_tail=0.08 floor=0 sel=32 7.8s
+    32/401 | loss=0.8537 ev=0.451 agents=34 avg_r=0.4553 sum_r=116.57 x<0=0.16 elig=0.59 dorfler_tail=0.07 floor=0 sel=33 7.9s
+    33/401 | loss=0.7271 ev=0.457 agents=193 avg_r=2.1602 sum_r=553.02 x<0=0.11 elig=0.59 dorfler_tail=0.08 floor=0 sel=31 7.7s
+    34/401 | loss=0.8864 ev=0.395 agents=132 avg_r=0.0379 sum_r=9.71 x<0=0.13 elig=0.60 dorfler_tail=0.07 floor=0 sel=31 7.6s
+    35/401 | loss=0.7846 ev=0.418 agents=60 avg_r=1.8461 sum_r=472.61 x<0=0.11 elig=0.59 dorfler_tail=0.08 floor=0 sel=30 7.5s
+    36/401 | loss=0.8040 ev=0.428 agents=139 avg_r=0.1920 sum_r=49.14 x<0=0.08 elig=0.59 dorfler_tail=0.07 floor=0 sel=29 7.5s
+    37/401 | loss=0.8225 ev=0.432 agents=228 avg_r=0.9105 sum_r=233.08 x<0=0.11 elig=0.59 dorfler_tail=0.07 floor=0 sel=30 7.6s
+    38/401 | loss=0.7612 ev=0.431 agents=34 avg_r=1.5990 sum_r=409.35 x<0=0.11 elig=0.60 dorfler_tail=0.07 floor=0 sel=31 7.7s
+    39/401 | loss=0.7474 ev=0.474 agents=60 avg_r=2.1517 sum_r=550.82 x<0=0.10 elig=0.60 dorfler_tail=0.07 floor=0 sel=29 7.4s
+    40/401 | loss=0.7913 ev=0.417 agents=228 avg_r=2.7027 sum_r=691.89 x<0=0.09 elig=0.59 dorfler_tail=0.08 floor=0 sel=33 7.8s
+    41/401 | loss=0.7976 ev=0.453 agents=199 avg_r=1.2828 sum_r=328.39 x<0=0.10 elig=0.60 dorfler_tail=0.07 floor=0 sel=28 7.3s
+    42/401 | loss=0.7862 ev=0.467 agents=40 avg_r=2.1315 sum_r=545.65 x<0=0.07 elig=0.60 dorfler_tail=0.07 floor=0 sel=30 7.5s
+    43/401 | loss=0.7528 ev=0.447 agents=34 avg_r=1.6585 sum_r=424.58 x<0=0.09 elig=0.60 dorfler_tail=0.07 floor=0 sel=30 7.5s
+    44/401 | loss=0.8170 ev=0.432 agents=193 avg_r=1.4874 sum_r=380.76 x<0=0.09 elig=0.60 dorfler_tail=0.07 floor=0 sel=31 7.6s
+    45/401 | loss=0.8174 ev=0.455 agents=230 avg_r=1.1440 sum_r=292.86 x<0=0.08 elig=0.60 dorfler_tail=0.07 floor=0 sel=29 7.3s
+    46/401 | loss=0.7965 ev=0.445 agents=34 avg_r=2.3036 sum_r=589.72 x<0=0.09 elig=0.60 dorfler_tail=0.07 floor=0 sel=30 7.5s
+    47/401 | loss=0.7296 ev=0.437 agents=120 avg_r=3.0991 sum_r=793.37 x<0=0.09 elig=0.59 dorfler_tail=0.07 floor=0 sel=30 7.4s
+    48/401 | loss=0.7574 ev=0.426 agents=34 avg_r=1.4336 sum_r=366.99 x<0=0.06 elig=0.60 dorfler_tail=0.07 floor=0 sel=30 7.4s
+    49/401 | loss=0.7115 ev=0.452 agents=314 avg_r=4.5889 sum_r=1174.75 x<0=0.09 elig=0.60 dorfler_tail=0.07 floor=0 sel=31 8.1s
+    50/401 | loss=0.8021 ev=0.447 agents=309 avg_r=1.0066 sum_r=257.70 x<0=0.08 elig=0.60 dorfler_tail=0.07 floor=0 sel=29 7.7s
+[Checkpoint] saved → checkpoints/model_iter0050.pt
+    51/401 | loss=0.7353 ev=0.461 agents=220 avg_r=2.4559 sum_r=628.70 x<0=0.08 elig=0.60 dorfler_tail=0.07 floor=0 sel=29 7.5s
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+[Checkpoint] saved → checkpoints/model_iter0100.pt
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+[Checkpoint] saved → checkpoints/model_iter0150.pt
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+[Checkpoint] saved → checkpoints/model_iter0200.pt
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+[Checkpoint] saved → checkpoints/model_iter0250.pt
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+[Checkpoint] saved → checkpoints/model_iter0300.pt
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+[Checkpoint] saved → checkpoints/model_iter0350.pt
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+   389/401 | loss=0.9674 ev=0.506 agents=1219 avg_r=2.7841 sum_r=712.73 x<0=0.01 elig=0.64 dorfler_tail=0.07 floor=0 sel=24 7.3s
+   390/401 | loss=1.0035 ev=0.524 agents=147 avg_r=7.6948 sum_r=1969.86 x<0=0.00 elig=0.64 dorfler_tail=0.08 floor=0 sel=32 8.5s
+   391/401 | loss=0.9791 ev=0.521 agents=749 avg_r=4.6773 sum_r=1197.40 x<0=0.01 elig=0.63 dorfler_tail=0.07 floor=0 sel=28 7.8s
+   392/401 | loss=1.0303 ev=0.538 agents=506 avg_r=5.7889 sum_r=1481.96 x<0=0.01 elig=0.63 dorfler_tail=0.08 floor=0 sel=30 7.9s
+   393/401 | loss=0.9156 ev=0.530 agents=34 avg_r=4.9215 sum_r=1259.91 x<0=0.01 elig=0.63 dorfler_tail=0.07 floor=0 sel=27 7.4s
+   394/401 | loss=0.9221 ev=0.550 agents=566 avg_r=6.1226 sum_r=1567.39 x<0=0.00 elig=0.63 dorfler_tail=0.08 floor=0 sel=30 7.9s
+   395/401 | loss=1.0507 ev=0.505 agents=278 avg_r=3.6668 sum_r=938.69 x<0=0.01 elig=0.63 dorfler_tail=0.07 floor=0 sel=28 7.5s
+   396/401 | loss=1.0621 ev=0.495 agents=535 avg_r=5.1409 sum_r=1316.06 x<0=0.02 elig=0.64 dorfler_tail=0.08 floor=0 sel=27 7.4s
+   397/401 | loss=0.8922 ev=0.549 agents=145 avg_r=5.6600 sum_r=1448.95 x<0=0.01 elig=0.64 dorfler_tail=0.08 floor=0 sel=29 7.9s
+   398/401 | loss=1.0484 ev=0.536 agents=62 avg_r=5.7253 sum_r=1465.68 x<0=0.02 elig=0.64 dorfler_tail=0.08 floor=0 sel=26 7.5s
+   399/401 | loss=1.0258 ev=0.542 agents=146 avg_r=6.1057 sum_r=1563.07 x<0=0.02 elig=0.64 dorfler_tail=0.08 floor=0 sel=29 7.8s
+   400/401 | loss=0.9834 ev=0.526 agents=697 avg_r=4.9534 sum_r=1268.06 x<0=0.02 elig=0.63 dorfler_tail=0.08 floor=0 sel=28 7.6s
+[Checkpoint] saved → checkpoints/model_iter0400.pt
+   401/401 | loss=0.9563 ev=0.563 agents=177 avg_r=7.3312 sum_r=1876.79 x<0=0.02 elig=0.64 dorfler_tail=0.08 floor=0 sel=30 7.9s
+[Checkpoint] saved → checkpoints/model_iter0401.pt
+[Checkpoint] saved → checkpoints/model_final.pt
+[Train] done, total time 3050.1s
+Training finished at Sat 30 May 16:07:16 CST 2026
diff --git a/output/__pycache__/build_pptx.cpython-310.pyc b/output/__pycache__/build_pptx.cpython-310.pyc
new file mode 100644
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diff --git a/output/__pycache__/build_pptx.cpython-313.pyc b/output/__pycache__/build_pptx.cpython-313.pyc
new file mode 100644
index 0000000..f3a1398
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diff --git a/output/build_pptx.py b/output/build_pptx.py
index 17e3c83..eb8500d 100644
--- a/output/build_pptx.py
+++ b/output/build_pptx.py
@@ -302,8 +302,8 @@ add_textbox(slide, Inches(0.6), Inches(4.2), Inches(12.1), Inches(0.4),
             font_color=BLACK, bold=True)
 
 innovations = [
-    ("[1] 无量纲化残差误差估计", "k_local 归一化三项残差分量，消除纯几何尺度偏差，跨介质公平可比", ACCENT_BLUE),
-    ("[2] Score-based 连续尺寸场", "score = -x_i 纯排序 + 物理预算约束 + Doerfler-P95 动作掩码", ACCENT_TEAL),
+    ("[1] 无量纲化残差误差估计", "真空波数 k 归一化残差+相位/空间特征+GVN，介质内 eta 不被压低", ACCENT_BLUE),
+    ("[2] Score-based 连续尺寸场", "score = -x_i 纯排序 + 物理预算约束 + Reverse Dörfler 动作掩码", ACCENT_TEAL),
     ("[3] L2 聚合奖励设计", "sqrt(sum eta_child^2) <= eta_parent 保证 r_local >= 0，永不惩罚细化", ACCENT_GREEN),
     ("[4] 尺度不变性架构", "N_init x domain_area + lambda 无量纲化特征 + ln 压缩 + 前渐近区约束", ACCENT_WARM),
 ]
@@ -366,9 +366,9 @@ add_textbox(slide, Inches(0.6), Inches(4.1), Inches(6.0), Inches(0.35),
             text="RL 问题建模", font_size=SUBHEAD_SIZE, font_color=BLACK, bold=True)
 rl_lines = [
     ("Agent = 每个三角形单元（数量动态变化，约 400 -> 20,000）", False, Pt(11), BODY_GRAY),
-    ("State = GNN 节点 12 维特征（几何 + PDE 残差 + 场量 + 物理参数）", False, Pt(11), BODY_GRAY),
+    ("State = GNN 节点 14 维特征（几何 + PDE 残差 + 振幅 + 相位方向 + 物理参数）", False, Pt(11), BODY_GRAY),
     ("Action = 1 维连续标量 x_i -> score = -x_i 排序 -> top-k 选择细化单元", False, Pt(11), BODY_GRAY),
-    ("Reward = L2 聚合局部改善 + 全局势函数塑形 - 动作惩罚", False, Pt(11), BODY_GRAY),
+    ("Reward = 零和预算审查: refined 获 r_local+0.3x(eta/mu-1)-0.06; unrefined r=0", False, Pt(11), BODY_GRAY),
 ]
 add_multiline_textbox(slide, Inches(0.6), Inches(4.5), Inches(6.0), Inches(2.0),
                       rl_lines, line_spacing=1.6)
@@ -378,7 +378,7 @@ add_textbox(slide, Inches(7.2), Inches(4.1), Inches(5.5), Inches(0.35),
             text="PPO 训练配置", font_size=SUBHEAD_SIZE, font_color=BLACK, bold=True)
 train_lines = [
     ("双 GNN 架构：Policy / Value 各自独立 MessagePassingBase", False, Pt(11), BODY_GRAY),
-    ("2 层消息传递，inner 残差 + LayerNorm，latent_dim=64", False, Pt(11), BODY_GRAY),
+    ("2 层消息传递 + GVN 全局虚拟节点 (注意力门控广播)，inner 残差 + LayerNorm，latent_dim=64", False, Pt(11), BODY_GRAY),
     ("DiagGaussian 连续动作分布，log_std 可学习，clamp [-4, -1]", False, Pt(11), BODY_GRAY),
     ("256 步 Rollout，5 Epochs，GAE lambda=0.95，lr=3e-4，梯度裁剪 0.5", False, Pt(11), BODY_GRAY),
 ]
@@ -399,17 +399,17 @@ add_slide_title(slide, "创新 [1]：无量纲化残差误差估计 -- 消除几
 add_textbox(slide, Inches(0.6), Inches(1.25), Inches(5.8), Inches(0.35),
             text="前序问题：原始残差包含 h_K、h_e 等几何尺度，不同区域不可直接比较", font_size=Pt(13), font_color=ACCENT_WARM)
 add_textbox(slide, Inches(0.6), Inches(1.55), Inches(5.8), Inches(0.35),
-            text="解决方案：引入局部波数 k_local 做无量纲归一化，反映相位分辨率残差", font_size=Pt(13), font_color=ACCENT_BLUE)
+            text="解决方案：改用真空波数 k 归一化，介质内残差不再被 sqrt(eps_r) 压低", font_size=Pt(13), font_color=ACCENT_BLUE)
 
 formulas = [
     ("内部残差 r_int",
-     "(h_K/k_local) * sqrt(V) * |k^2*eps_r*u + k^2*(eps_r-1)*u_inc|_K",
-     "单元内部 PDE 残差；除以 k_local 使大 eps_r 介质区与真空区可比"),
+     "(h_K/k) * sqrt(V) * |k^2*eps_r*u + k^2*(eps_r-1)*u_inc|_K",
+     "单元内部 PDE 残差；真空波数 k 归一化；SBC 条件保留 k_local"),
     ("梯度跳变 r_jump",
-     "sqrt(1/2 * sum_{e in dK} (h_e/k_local) * |[[grad u * n]]|^2_e)",
-     "相邻单元梯度跳变；h_e/k_local 使细化后跳变自然衰减"),
+     "sqrt(1/2 * sum_{e in dK} (h_e/k) * |[[grad u * n]]|^2_e)",
+     "相邻单元梯度跳变；h_e/k 使细化后跳变自然衰减"),
     ("SBC 边界 r_sbc",
-     "(h_bnd/k_local) * |du/dn - i*k_local*u|",
+     "(h_bnd/k) * |du/dn - i*k_local*u|",
      "Sommerfeld 吸收边界残差，仅在边界单元非零"),
 ]
 
@@ -438,13 +438,13 @@ add_textbox(slide, Inches(7.5), Inches(4.0), Inches(5.0), Inches(0.55),
 add_textbox(slide, Inches(0.6), Inches(4.85), Inches(12.1), Inches(0.3),
             text="量纲分析验证", font_size=SUBHEAD_SIZE, font_color=BLACK, bold=True)
 da_lines = [
-    ("k_local ~ [L]^-1, h_e ~ [L], |jump|^2 ~ [L]^-2  =>  h_e/k_local * |jump|^2 ~ [L]^2 * [L]^-2 = 1  严格无量纲", False, Pt(11), BODY_GRAY),
+    ("k_local ~ [L]^-1, h_e ~ [L], |jump|^2 ~ [L]^-2  =>  h_e/k * |jump|^2 ~ [L]^2 * [L]^-2 = 1  严格无量纲", False, Pt(11), BODY_GRAY),
     ("GNN 输入用 log10 压缩的特征；Reward 用原始 eta_K（不经 log 压缩），两者公式一致，物理语义对齐", False, Pt(11), BODY_GRAY),
 ]
 add_multiline_textbox(slide, Inches(0.6), Inches(5.15), Inches(12.1), Inches(0.8),
                       da_lines, line_spacing=1.5)
 
-add_takeaway_bar(slide, "k_local 归一化使误差指示子反映相位分辨率残差而非网格粗疏程度，为 RL agent 提供物理一致的误差信号")
+add_takeaway_bar(slide, "真空波数 k 归一化使介质内残差自然放大 ~sqrt(eps_r) 倍，为 RL agent 提供正确的介质内/外优先级信号")
 add_slide_number(slide, 5)
 
 
@@ -453,7 +453,7 @@ add_slide_number(slide, 5)
 # ======================================================================
 slide = add_blank_slide()
 set_slide_bg(slide, WHITE)
-add_slide_title(slide, "创新 [2]：12 维增强输入特征 -- 赋予 GNN 几何与物理感知")
+add_slide_title(slide, "创新 [2]：14 维增强输入特征 -- 赋予 GNN 振幅与相位方向感知")
 
 add_textbox(slide, Inches(0.6), Inches(1.25), Inches(12.1), Inches(0.35),
             text="前序 11 维 -> 现 12 维，新增 dist_to_interface。全部尺度相关特征均以真空波长 lambda=2*pi/k 无量纲化", font_size=Pt(13), font_color=ACCENT_BLUE)
@@ -479,7 +479,7 @@ features = [
     ("element_penalty", "单元惩罚系数 lambda", "--"),
     ("timestep", "当前 rollout 步数", "--"),
     ("wave_number", "Helmholtz 波数 k", "--"),
-    ("k_local_sqrt_vol", "k_local x sqrt(volume) 已无量纲", "--"),
+    ("k_local_sqrt_vol", "k x sqrt(eps_r) x sqrt(volume)", "--"),
     ("is_sbc_boundary", "是否与 SBC 边界相邻 (0/1)", "--"),
     ("dist_to_interface", "到介质边界的带符号距离 [新增]", "sign(d)*ln(1+|d|/lambda)"),
     ("epsilon_r", "单元中点介电常数（内=eps_r, 外=1.0）", "--"),
@@ -501,7 +501,7 @@ for i, (name, meaning, norm) in enumerate(features):
 
 # Edge feature note — positioned after table (table bottom = 1.65 + 0.30 + 12*0.30 = 5.55")
 add_textbox(slide, Inches(0.6), Inches(5.65), Inches(12.1), Inches(0.25),
-            text="边特征 (1 维)：euclidean_distance / lambda -- 相邻单元中点无量纲距离  |  合计：12 (节点) + 1 (边) = 13 维图特征",
+            text="边特征 (1 维)：euclidean_distance / lambda -- 相邻单元中点无量纲距离  |  合计：14 (节点) + 1 (边) = 15 维图特征",
             font_size=Pt(9), font_color=BODY_GRAY)
 
 add_takeaway_bar(slide, "全部与尺度相关的特征均以 lambda 做无量纲归一化；dist_to_interface 用 sign·ln(1+|d|) 对数压缩，近场线性、远场自然压缩，与残差 log10 风格统一")
@@ -534,7 +534,7 @@ algo_steps = [
     ("Step 2: Score 排序",
      "score = -x_i  (Actor 输出标量)\nx 越小 -> 优先级越高，纯排序，不设正负门槛"),
     ("Step 3: 双过滤器",
-     "eligible = {i | area_i > 0.25 x A_budget_i  AND  eta_i >= 0.05 x eta_P95}\narea_floor: 排除已足够细的单元\nDoerfler-P95: 排除低误差单元 (P95 锚定物理误差尺度)"),
+     "eligible = {i | area_i > V_min_safeguard  AND  i in Reverse_Dorfler_set}\narea_floor: 纯数值底线 (1e-10 x domain_area)\nReverse Dorfler: 能量尾部淘汰 (eps_noise=0.01, >=20% floor)"),
     ("Step 4: Top-k 选择",
      "num = min(|eligible|, N_current//4, remaining//3)    (自适应 cap, 增速 N//4)\nselected = top-k by score -> 1-to-4 切分细化"),
 ]
@@ -549,10 +549,10 @@ for i, (title, content) in enumerate(algo_steps):
 add_rect(slide, Inches(0.6), Inches(5.45), Inches(12.1), Inches(0.95), fill_color=None,
          line_color=ACCENT_BLUE, line_width=Pt(0.5))
 add_textbox(slide, Inches(0.8), Inches(5.5), Inches(11.7), Inches(0.85),
-            text="为什么用 Doerfler-P95 而非 median/mean？P95 锚定物理误差尺度，免疫远场噪声稀释。远场低 eta 区即使占 90% 的单元，也不会拉低锚点。确保只有误差真正达标的区域才消耗细化预算。",
+            text="为什么用 Reverse Dörfler 而非 P95 硬阈值？P95 在重尾分布下会被奇异点推至极高，一刀切屏蔽大片中等误差区域。Reverse Dörfler 基于能量累积 (L2 范数平方和)，自适应于任意分布形态，剔除确认无价值的底部噪声，保留 >=20% 单元确保 Agent 选择空间。",
             font_size=Pt(11), font_color=BODY_GRAY)
 
-add_takeaway_bar(slide, "Score-based 排序 + 物理预算 + Doerfler-P95 掩码：三层保障确保细化资源只投入到物理上需要的地方")
+add_takeaway_bar(slide, "Score-based 排序 + 物理预算 + Reverse Dörfler 掩码：三层保障确保细化资源只投入到物理上需要的地方")
 add_slide_number(slide, 7)
 
 
@@ -608,16 +608,17 @@ add_multiline_textbox(slide, Inches(0.6), Inches(4.8), Inches(6.0), Inches(0.7),
                       pen_lines, line_spacing=1.5)
 
 add_textbox(slide, Inches(7.2), Inches(4.45), Inches(5.5), Inches(0.3),
-            text="全局势函数塑形", font_size=SUBHEAD_SIZE, font_color=BLACK, bold=True)
+            text="Actor 奖励设计原则", font_size=SUBHEAD_SIZE, font_color=BLACK, bold=True)
 glob_lines = [
-    ("E_global = sqrt(sum eta_K^2) / ||u_h||_{L2(Omega)}    (无量纲全局误差)", False, Pt(12), BODY_GRAY),
-    ("global_bonus = alpha x [log(E_old) - log(E_new)],  alpha = 0.2", False, Pt(12), BODY_GRAY),
-    ("仅发给被细化的父单元 -- 避免被未细化单元稀释信号", False, Pt(11), CAPTION),
-]
+        ("global_bonus 被 Helmholtz 污染误差污染", False, Pt(12), BODY_GRAY),
+        ("E_new > E_old 可发生在正确细化后", False, Pt(11), BODY_GRAY),
+        ("惩罚 Agent 做对的事 → 策略崩塌 (x<0→0.01)", False, Pt(11), BODY_GRAY),
+        ("修正: global_bonus 仅诊断, 不注入 Actor reward", False, Pt(11), CAPTION),
+    ]
 add_multiline_textbox(slide, Inches(7.2), Inches(4.8), Inches(5.5), Inches(0.7),
                       glob_lines, line_spacing=1.5)
 
-add_takeaway_bar(slide, "奖励公式 = L2 聚合局部改善 (>=0) + 全局势函数塑形 (仅细化单元) - 轻微动作惩罚 -> 每个被细化父单元净奖励约 +0.387")
+add_takeaway_bar(slide, "零和预算审查: 奖金 0.3*(eta/mu-1) 全场求和为零 (Doerfler 准则 RL 对偶); unrefined r=0; global_bonus 仅诊断")
 add_slide_number(slide, 8)
 
 
@@ -771,12 +772,14 @@ add_textbox(slide, Inches(0.8), Inches(1.85), Inches(5.4), Inches(0.3),
             text="MessagePassingBase (x2, Policy / Value 各自独立基座)", font_size=Pt(13), font_color=ACCENT_BLUE, bold=True)
 
 gnn_items = [
-    ("节点嵌入", "Linear(12 -> 64)"),
+    ("节点嵌入", "Linear(14 -> 64)"),
     ("边嵌入", "Linear(1 -> 64)"),
     ("MP Step 1", "EdgeModule: MLP([src|dst|edge_attr]) -> 64d"),
     ("", "NodeModule: MLP([node|scatter_mean(入边)]) -> 64d"),
     ("", "+ inner 残差 + LayerNorm"),
     ("MP Step 2", "同 Step 1，堆叠 2 层"),
+    ("GVN 全局虚拟节点", "h_V = Σ(η_v/Ση)·h_v (η_K 加权池化)"),
+    ("", "α = σ(W[h_v||h_V])，h_v += scale·α ⊙ W_V·h_V"),
     ("输出", "节点隐向量 (num_nodes, 64)"),
 ]
 
@@ -896,10 +899,10 @@ add_slide_title(slide, "创新点汇总与可复用价值")
 
 innovations = [
     ("[1]", "无量纲化\n残差误差估计",
-     "k_local 归一化三项残差分量\n消除纯几何尺度偏差\nGNN 输入与 Reward 公式物理一致",
+     "真空波数 k 归一化残差\n介质内 η 不再被压低\nGNN+Reward 统一使用 k 归一化",
      ACCENT_BLUE),
     ("[2]", "Score-based\n连续尺寸场",
-     "score = -x_i 纯排序\n物理预算 N_budget 约束\nDoerfler-P95 双过滤器掩码",
+     "score = -x_i 纯排序\n物理预算 N_budget 约束\nReverse Dörfler 双过滤器掩码",
      ACCENT_TEAL),
     ("[3]", "L2 聚合\n奖励设计",
      "sqrt(sum eta_child^2) <= eta_parent 天然成立\n永不惩罚细化 (r_local >= 0)\nint 主导区强正奖励约 +0.69",
@@ -927,9 +930,9 @@ add_textbox(slide, Inches(0.6), Inches(4.7), Inches(12.1), Inches(0.3),
 
 reuse_items = [
     ("L2 聚合 + 父子映射", "适用于任何分裂型变长 agent RL 场景（网格细化、树搜索、层次化决策）"),
-    ("k_local 无量纲化方法", "适用于具有特征尺度的任何 PDE 问题：跨介质、跨频率、跨几何的统一误差度量"),
+    ("真空波数 k 归一化方法", "残差归一化用 k₀ 非 k_local，介质内物理信号不再被压低"),
     ("Score-based + 预算约束选择", "适用于资源受限的排序-选择问题：传感器部署、计算资源分配、实验设计优化"),
-    ("Doerfler-P95 动作掩码", "P95 锚定物理尺度的思想可推广到任何需要排除低信号样本的场景"),
+    ("Reverse Dörfler 动作掩码", "能量尾部淘汰的思想可推广到任何需要排除低信号样本的场景"),
 ]
 for i, (tag, desc) in enumerate(reuse_items):
     add_textbox(slide, Inches(0.8), Inches(5.05 + i * 0.42), Inches(2.8), Inches(0.35),
@@ -1002,8 +1005,8 @@ add_textbox(slide, Inches(0.85), Inches(2.0), Inches(11.5), Inches(1.0),
 
 summary_points = [
     "提出了一套完整的 RL 自适应网格细化框架：从物理建模、误差估计、状态表征、动作空间到奖励设计的全链路创新",
-    "无量纲化残差误差估计 (k_local 归一化) 使误差指示子具有跨介质、跨频率的物理一致性",
-    "Score-based 尺寸场 + 物理预算约束 + Doerfler-P95 掩码实现了资源感知的细化单元选择",
+    "真空波数 k 归一化残差使介质内 η 自然放大，Agent 获得正确的物理优先级信号",
+    "Score-based 尺寸场 + 物理预算约束 + Reverse Dörfler 掩码实现了资源感知的细化单元选择",
     "L2 聚合奖励设计从数学上保证了细化奖励非负，从根本上避免了 L1 sum 的结构性负偏置",
     "sign(d)*ln(1+|d|/lambda) 对数压缩 + lambda 归一化全部特征实现了域尺寸的尺度不变泛化",
 ]
diff --git a/output/final_presentation_cn.pptx b/output/final_presentation_cn.pptx
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diff --git a/paper_outline.md b/paper_outline.md
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+++ b/paper_outline.md
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+# 论文大纲框架
+
+**暂定标题（中文）：** 基于图神经网络与强化学习的亥姆霍兹散射问题自适应网格细化
+
+**暂定标题（英文）：** Reinforcement Learning–Driven Adaptive Mesh Refinement for 2D Helmholtz Scattering via Graph Neural Networks
+
+---
+
+## 1. Introduction（引言）
+
+### 1.1 领域背景与重要性
+- 高频亥姆霍兹方程在电磁散射、声学等领域的重要性
+- 有限元方法（FEM）求解亥姆霍兹问题的挑战：污染效应（pollution effect），即标准FEM在高频下误差随波数增长
+
+### 1.2 现有方法与瓶颈
+- 自适应网格细化（AMR）的传统方法：基于残差的误差指示器、Dörfler标记策略
+- 传统AMR的局限性：启发式标记策略难以捕获全局误差分布；高频问题中局部指标与全局误差脱节
+- 已有的机器学习方法尝试（如有相关工作）
+
+### 1.3 本文贡献（Gap → Solution）
+- 提出将AMR建模为马尔可夫决策过程（MDP），使用PPO训练GNN策略网络
+- 三个核心创新点：
+  - （a）空间奖励函数设计，考虑网格细化层级映射
+  - （b）全局虚拟节点（GVN）GNN架构，突破消息传递的直径瓶颈
+  - （c）物理信息特征（相位距离、局部波数）提升泛化能力
+
+### 1.4 论文组织
+- 简述后续各节安排
+
+---
+
+## 2. Problem Formulation（问题形式化）
+
+### 2.1 亥姆霍兹散射问题的数学描述
+- 控制方程：$\nabla^2 u_{scat} + k^2 \epsilon_r u_{scat} = k^2(1-\epsilon_r)u_{inc}$
+- Sommerfeld辐射边界条件
+- P1三角单元的FEM离散
+
+### 2.2 残差误差指示器
+- $\eta_K$ 的定义：内部残差 + 梯度跳跃 + SBC边界项
+- 误差指示器的物理意义
+
+### 2.3 AMR作为序贯决策问题
+- 为什么传统的单步标记策略不够
+- 将多步细化过程建模为MDP的理由
+
+---
+
+## 3. Method（方法）
+
+### 3.1 RL Environment（强化学习环境）
+
+#### 3.1.1 状态空间（State）
+- 图表示：节点 = 网格单元，边 = 邻接关系
+- 节点特征（13维）：几何、残差、解信息、时间步
+- 边特征（1维）：相位距离
+
+#### 3.1.2 动作空间（Action）
+- 连续评分，基于排序选择top-k细化
+
+#### 3.1.3 奖励函数（Reward）
+- 基于 $\log(\eta_{old}) - \log(\eta_{new})$ 的对数误差缩减
+- 零和奖励项（Dörfler准则的软实现）
+- 元素数惩罚项 $\lambda \cdot (N_{new} - 1)$
+
+#### 3.1.4 预算约束
+- $N_{budget} \propto k^2$
+
+### 3.2 GNN Policy Architecture（GNN策略架构）
+
+#### 3.2.1 消息传递基座
+- 2层边更新 + 节点更新
+- 残差连接 + LayerNorm
+
+#### 3.2.2 全局虚拟节点（GVN）
+- 注意力门控池化
+- 注入全局误差分布上下文，突破消息传递的直径瓶颈
+
+#### 3.2.3 Actor-Critic头
+- 分离的策略头和价值头
+- Actor：对角高斯分布
+- Critic：节点级价值聚合
+
+### 3.3 PPO Training（PPO训练）
+- 自定义RolloutBuffer处理可变智能体数量（网格细化导致节点数变化）
+- GAE计算中使用scatter_add将子节点价值投影回父节点
+- 标准PPO裁剪损失 + 熵正则化
+
+---
+
+## 4. Experiments（实验）
+
+### 4.1 Experimental Setup（实验设置）
+- 数值求解器：scikit-fem，P1三角单元
+- 训练配置：401次迭代，256步rollout
+- 初始网格：基于波数 $k$ 和域面积自动缩放（$N \propto k^2$）
+- 预渐近约束：$h \leq \lambda_d / 1.5$
+
+### 4.2 Baselines（基线方法）
+- 均匀细化（Uniform refinement）
+- 基于残差误差指示器的传统AMR（Dörfler标记）
+- 随机策略（Random policy）
+- （如有其他消融实验变体）
+
+### 4.3 Main Results（主要结果）
+- 不同波数 $k$ 下的误差收敛曲线（error vs. DOF）
+- 不同散射体几何（圆形、多圆形、方形）的泛化性能
+- 网格演化可视化（refinement pattern）
+
+### 4.4 Ablation Studies（消融实验）
+- 奖励函数设计的影响（有/无零和奖励、有/无元素数惩罚）
+- GVN模块的贡献（有/无全局上下文）
+- 物理信息特征（相位距离）的影响
+- 消息传递层数的影响
+
+### 4.5 Analysis & Diagnostics（分析与诊断）
+- 学到的细化模式分析（是否集中在散射体边界/高梯度区域）
+- 动作分布统计（$x<0$ 比率的变化趋势）
+- 训练曲线（奖励、误差缩减、元素数的收敛过程）
+
+---
+
+## 5. Discussion（讨论）
+
+- **核心优势**：RL策略能够学习超越传统启发式的全局细化模式
+- **与传统方法的关系**：学到的策略隐式地实现了类似Dörfler的标记，但具有更强的上下文感知
+- **GVN的作用**：全局信息对高频问题中跨域误差传播的关键性
+- **局限性**：
+  - 当前仅限2D亥姆霍兹问题
+  - P1单元的固有色散误差未被修正
+  - 训练成本较高
+- **未来方向**：
+  - 双加权残差（DWR）：引入伴随误差估计以获得更准确的奖励信号
+  - 相空间方法：使用Wigner分布引导基于动量失配的细化
+  - 算子修正：探索Trefftz方法或GLS稳定化以减少P1单元的固有色散误差
+
+---
+
+## 6. Conclusion（结论）
+
+- 贡献总结：将AMR建模为RL问题，设计了空间奖励函数和GVN-GNN架构
+- 关键证据：在多个波数和几何上展示了误差收敛优势
+- 影响：为高频波传播问题的数据驱动网格优化提供了新范式
+- 边界：当前框架的适用范围与假设
+
+---
+
+## 补充说明
+
+| 项目 | 说明 |
+|---|---|
+| 论文类型 | 方法论文（Method paper） |
+| 核心主张 | RL+GNN可以学习优于传统启发式的AMR策略，尤其在高频亥姆霍兹问题中 |
+| 证据支撑 | 误差收敛曲线、不同几何泛化、消融实验、网格演化可视化 |
+| 待确认 | 是否有与传统AMR的定量对比数据？是否有跨波数泛化的实验？GVN消融结果如何？ |
diff --git a/paper_outline.tex b/paper_outline.tex
new file mode 100644
index 0000000..578636b
--- /dev/null
+++ b/paper_outline.tex
@@ -0,0 +1,466 @@
+\documentclass[11pt,a4paper]{article}
+
+% ---- 基础包 ----
+\usepackage[utf8]{inputenc}
+\usepackage[T1]{fontenc}
+\usepackage{amsmath,amssymb,amsfonts}
+\usepackage{graphicx}
+\usepackage{booktabs}
+\usepackage{hyperref}
+\usepackage[margin=2.5cm]{geometry}
+\usepackage{enumitem}
+\usepackage{xcolor}
+
+% ---- 实验标注命令 ----
+\newcommand{\needexp}[1]{\textcolor{red}{[实验待做: #1]}}
+
+% ---- 标题信息 ----
+\title{基于图神经网络与强化学习的亥姆霍兹散射问题自适应网格细化：\\
+跨波数零样本泛化与非局域误差传播}
+\author{[作者姓名] \\ [单位]}
+\date{}
+
+\begin{document}
+
+\maketitle
+
+% ============================================================
+\section{Introduction（引言）}
+% ============================================================
+
+\subsection{领域背景（Field Scale）}
+
+\begin{itemize}
+  \item 高频亥姆霍兹方程 $\nabla^2 u + k^2\varepsilon_r u = f$ 是电磁散射、声学传播、地震成像等领域的核心控制方程
+  \item 有限元方法（FEM）求解亥姆霍兹问题的核心困难：\textbf{污染效应（pollution effect）}——标准 P1 Galerkin FEM 的色散误差随波数 $k$ 增大而累积，导致"即使每波长分辨率足够，远场相位误差仍不可接受"
+  \item 缓解污染效应的主要手段：\textbf{自适应网格细化（AMR）}——在有物理特征（介质界面、高梯度区）的地方局部加密网格，在平缓区保持粗网格
+\end{itemize}
+
+\subsection{现有方法与瓶颈（Prior Attempts \& Bottleneck）}
+
+\begin{itemize}
+  \item \textbf{传统 AMR：}基于后验误差估计子（残差型 $\eta_K$、梯度恢复型）的单步启发式标记策略（D\"{o}rfler 标记、最大策略标记）
+  \item \textbf{传统方法的两个根本局限：}
+    \begin{enumerate}
+      \item \textbf{贪心单步决策}：每步仅根据当前误差分布标记细化区域，无法规划多步预算分配——早期过度细化低价值区域会耗尽后续步的预算
+      \item \textbf{局部信息盲区}：高频亥姆霍兹的误差通过波动物理在长距离上非局域传播（介质界面的误差影响远场散射场），而传统误差指示子仅反映局部残差，无法感知误差的因果来源
+    \end{enumerate}
+  \item \textbf{已有 ML-AMR 方法：}Adaptive Swarm Mesh Refinement (ASMR) 首次将 AMR 形式化为多智能体 MDP 并用 PPO 训练 GNN 策略，但：
+    \begin{itemize}
+      \item 针对泊松/椭圆型方程（自伴、椭圆、误差局部扩散），消息传递机制在椭圆型设置下足够
+      \item 未涉及高频亥姆霍兹方程的非局域性、不定号性和污染效应
+    \end{itemize}
+\end{itemize}
+
+\subsection{未解决的核心 gap（Unresolved Gap）}
+
+\begin{itemize}
+  \item 高频亥姆霍兹散射中的非局域误差传播要求网格细化策略具备\textbf{全局上下文感知能力}——标准 GNN 的局部消息传递受限于图的直径，需 $O(\text{diameter})$ 层数才能传递远距离信息
+  \item 传统 AMR 的误差指示子和标记阈值是\textbf{$k$ 相关的}——针对某个波数调好的参数在更高频段失效，需要重新调参
+  \item 已有方法需依赖真值或超精细网格参考解作为训练信号——在实际工程中通常不可得
+\end{itemize}
+
+\subsection{本文贡献（Present Study）}
+
+提出一种针对高频亥姆霍兹散射的 RL-GNN 自适应网格细化方法。核心贡献：
+
+\begin{enumerate}[label=\textbf{C\arabic*}, leftmargin=*]
+  \item \textbf{首次将 RL-AMR 拓展到高频亥姆霍兹方程。}通过全局虚拟节点（GVN）架构解决非局域误差传播问题，使得 GNN 策略能感知全局误差分布。
+  \item \textbf{跨波数零样本泛化。}通过 $k$ 不变特征归一化（真空波数归一化 + 相位距离边特征），策略在中等波数 $k\in[3,15]$ 训练后可直接泛化到更高波数 $k=30$——无需重新调参或微调。传统 AMR 方法无法做到这一点。
+  \item \textbf{残差型后验误差估计子 $\eta_K$ 作为奖励信号。}无需解析解或超精细参考网格，使方法可应用于任意散射体几何和介质分布。
+  \item \textbf{因果隔离的奖励函数设计。}通过 agent\_mapping 追踪父子元素层级，保证奖励信号的因果正确性：全局误差变化不反馈给 Actor，未细化父元素获得零奖励。
+\end{enumerate}
+
+\subsection{论文组织}
+
+第 2 节建立问题形式化，第 3 节详述方法，第 4 节给出实验与消融分析，第 5 节讨论与展望，第 6 节总结。
+
+% ============================================================
+\section{Problem Formulation（问题形式化）}
+% ============================================================
+
+\subsection{亥姆霍兹散射问题}
+
+\textbf{控制方程（二维）：}
+\begin{equation}
+  \nabla^2 u_{\mathrm{scat}} + k^2 \varepsilon_r(\mathbf{x}) u_{\mathrm{scat}}
+  = k^2\big(1-\varepsilon_r(\mathbf{x})\big) u_{\mathrm{inc}}(\mathbf{x})
+  \label{eq:helmholtz}
+\end{equation}
+
+其中 $u_{\mathrm{scat}}$ 为散射场，$u_{\mathrm{inc}}$ 为入射平面波，$k$ 为真空波数，$\varepsilon_r(\mathbf{x})$ 为相对介电常数分布。外边界施加一阶 Sommerfeld 辐射条件：
+\begin{equation}
+  \frac{\partial u_{\mathrm{scat}}}{\partial n} - i k u_{\mathrm{scat}} = 0
+  \label{eq:sbc}
+\end{equation}
+
+\textbf{散射体：}圆形介质柱（$\varepsilon_r \in [2.0, 8.0]$），半径和位置可随机化。计算域为 $[0,1] \times [0,1]$ 矩形。
+
+\textbf{FEM 离散：}P1 线性三角单元。Galerkin 弱形式：
+\begin{equation}
+  \int_\Omega \nabla u_h \cdot \nabla v_h \,dx
+  - k^2\int_\Omega \varepsilon_r u_h v_h \,dx
+  - ik\oint_{\partial\Omega} u_h v_h \,ds
+  = -k^2\int_\Omega (1-\varepsilon_r)u_{\mathrm{inc}} v_h \,dx
+\end{equation}
+
+\subsection{残差型后验误差估计子 $\eta_K$}
+
+对每个三角单元 $K$，定义无量纲残差误差指示子（以真空波数 $k$ 归一化，\textbf{非}局部波数 $k\sqrt{\varepsilon_r}$）：
+
+\begin{equation}
+  \eta_K^2 =
+  \underbrace{\left(\frac{h_K}{k}\right)^2 \cdot V_K \cdot \big|k^2\varepsilon_r u_h + k^2(\varepsilon_r-1)u_{\mathrm{inc}}\big|^2}_{\text{内部残差}}
+  + \underbrace{\frac{1}{2}\sum_{e\in\partial K} \frac{h_e}{k} \cdot \big\|[\kern-2pt[ \nabla u_h\cdot\mathbf{n} ]\kern-2pt]\big\|^2_e}_{\text{梯度跳跃}}
+  + \underbrace{\frac{h_{\mathrm{bnd}}}{k} \cdot \big|\frac{\partial u_h}{\partial n} - ik u_h\big|^2}_{\text{SBC 边界残差}}
+  \label{eq:eta}
+\end{equation}
+
+\textbf{为什么用真空波数归一化：}使用局部波数 $k_{\mathrm{local}} = k\sqrt{\varepsilon_r}$ 会导致介质内部 $\eta_K$ 被人为压制 $\sqrt{\varepsilon_r}$ 倍，使 GNN 对介质内部区域"视而不见"。用真空波数 $k$ 保证不同介质区域的误差指示子可比。
+
+\textbf{为什么用 $\eta_K$ 作为奖励而非真值：}在实际散射问题中，不存在解析解或超精细参考解。$\eta_K$ 是仅依赖当前 FEM 解的可计算量，且在预渐近条件下（$h \leq \lambda_d/N$）与真实误差等价（可靠性 + 有效性）。这使得整个方法不绑定任何特定几何或介质。
+
+\subsection{预渐近约束（Pre-asymptotic Resolution）}
+
+在细化开始前，强制介质内部单元满足 $h_K \leq \lambda_d / N$（$N=1.5$，$\lambda_d = 2\pi/(k\sqrt{\varepsilon_r})$ 为介质内波长），确保初始网格已充分解析介质内部波的相位变化。该约束防止 GNN 从"纯数值噪声"中学习。
+
+\subsection{AMR 作为序贯决策问题}
+
+将 $T$ 步网格细化过程形式化为 MDP $\langle \mathcal{S}, \mathcal{A}, P, R, \gamma \rangle$：
+
+\begin{itemize}
+  \item \textbf{状态 $\mathcal{S}$：}图 $\mathcal{G}_t = (\mathcal{V}_t, \mathcal{E}_t)$，节点为三角单元，边为共享棱边的邻接关系。节点特征 13 维，边特征 1 维（相位距离，见 \S\ref{sec:features}）
+  \item \textbf{动作 $\mathcal{A}$：}每个单元输出连续评分 $x_i \in \mathbb{R}$，按 $\mathrm{score}_i = -x_i$ 降序排列，在物理预算 $N_{\mathrm{budget}} \propto k^2$ 约束下选择 top-$k$ 单元进行细化（Rivara 最长边二分 + 一致性闭包）
+  \item \textbf{奖励 $R$：}基于 $\eta_K$ 的对数误差缩减（见 \S\ref{sec:reward}）
+  \item \textbf{终止：}达到最大步数 $T_{\max}=4\sim6$，或预算耗尽，或网格总单元数超过上限（50k）
+  \item \textbf{关键区别（vs 传统 AMR）：}策略可以跨步规划——在早期步骤有意保留预算，在后期步骤集中处理高价值区域
+\end{itemize}
+
+% ============================================================
+\section{Method（方法）}
+% ============================================================
+
+\subsection{$k$ 不变特征设计}
+\label{sec:features}
+
+为使 GNN 在不同波数 $k$ 下看到相似分布的输入，所有特征均设计为 $k$ 无关或 $k$ 尺度化的形式。
+
+\textbf{节点特征（13 维）：}
+\begin{enumerate}[leftmargin=*]
+  \item 单元体积 $V_K$（经过对数压缩）
+  \item--4. 三个残差分量：$\log(1 + \eta_{K,\mathrm{int}})$, $\log(1 + \eta_{K,\mathrm{jump}})$, $\log(1 + \eta_{K,\mathrm{bnd}})$
+  \item 惩罚项标志（是否属于细化惩罚区）
+  \item 当前时间步 $t/T_{\max}$
+  \item $k\sqrt{V_K}$：波数-尺度耦合特征
+  \item SBC 边界标志：单元是否接触 Sommerfeld 边界
+  \item 到介质界面的有符号对数距离：$\mathrm{sign}(d) \cdot \log(1 + |d|)$
+  \item $\varepsilon_r$：单元所在介质的相对介电常数
+  \item 场幅值：$|u_h|$
+  \item--13. 复场的相位特征：$\cos(\angle u_h)$, $\sin(\angle u_h)$
+\end{enumerate}
+
+\textbf{边特征（1 维）：}
+\begin{equation}
+  e_{ij} = k \cdot |\mathbf{x}_i^{\mathrm{mid}} - \mathbf{x}_j^{\mathrm{mid}}| \pmod{2\pi}
+\end{equation}
+即两个相邻单元中点之间的相位距离。该特征是 $k$ 自适应的——在更高波数下，物理波长更短，中点距离自然更大（以相位度量）。以此保证跨波数下边特征的分布一致。
+
+\subsection{奖励函数设计：因果隔离 + 零和预算审计}
+\label{sec:reward}
+
+奖励函数的核心原则：
+
+\begin{enumerate}[leftmargin=*]
+  \item \textbf{基于 $\eta_K$ 而非真值}（如上所述）
+  \item \textbf{因果隔离：}仅被细化的父元素获得奖励，未细化的父元素获得零奖励。全局误差变化不反馈给 Actor——因为高频亥姆霍兹的远场误差受介质内部多个区域共同影响，将全局误差直接分配给局部动作会破坏因果关系
+  \item \textbf{零和预算审计：}受 D\"{o}rfler 标记策略启发，引入零和奖励项——$\eta_K$ 高于均值的元素获得正奖励，低于均值的元素获得等量负惩罚。保证整体预算中性
+\end{enumerate}
+
+\textbf{奖励计算公式：}
+\begin{equation}
+  r_i = \underbrace{\log\eta_{K,i}^{\mathrm{old}} - \max_{j \in \mathrm{children}(i)} \log\eta_{K,j}^{\mathrm{new}}}_{\text{对数误差缩减}}
+      + \underbrace{\alpha \cdot \big(\eta_{K,i} - \bar{\eta}_K\big)}_{\text{零和 D\"{o}rfler 奖励}}
+      - \underbrace{\lambda \cdot (n_i^{\mathrm{children}} - 1)}_{\text{元素数惩罚}}
+\end{equation}
+
+其中 $\mathrm{children}(i)$ 通过 \texttt{agent\_mapping} $\phi_{ij}$ 将子元素误差映射到父元素，取 $\max$（最差子元素决定奖励，驱动策略优先处理最难改善的区域）。
+
+\textbf{奖励归一化：}每个 rollout 内对所有 agent 的奖励做 z-score 标准化，移除 reward scale 对 PPO 更新的影响。
+
+\subsection{GNN 策略架构}
+
+\subsubsection{消息传递基座（MessagePassingBase）}
+
+\begin{itemize}
+  \item 节点特征嵌入：Linear(13, 64) + Tanh
+  \item 边特征嵌入：Linear(1, 64) + Tanh
+  \item \texttt{MessagePassingStack}：2 层 $\{\text{EdgeModule} \to \text{NodeModule}\}$
+    \begin{itemize}
+      \item EdgeModule：聚合相邻节点特征 $h_i, h_j$ 与边特征 $e_{ij}$，更新边表征
+      \item NodeModule：聚合邻边表征，更新节点表征
+      \item 每层内部含残差连接 + LayerNorm
+    \end{itemize}
+  \item 训练时 Edge Dropout = 0.1
+\end{itemize}
+
+\subsubsection{全局虚拟节点（Global Virtual Node, GVN）}
+
+\textbf{设计动机：}标准消息传递 GNN 的信息传播受限于图的直径——要在相距 $d$ 跳的两个节点间传递信息，至少需要 $d$ 层消息传递。对于高频亥姆霍兹问题，介质界面的误差通过波传播影响远场，需要全局上下文。GVN 提供 $O(1)$ 的全局信息通道。
+
+\textbf{GVN 机制：}
+\begin{enumerate}[leftmargin=*]
+  \item \textbf{池化：}对所有节点特征做误差加权池化，得到全局上下文向量 $g$：
+    \begin{equation}
+      g = \sum_{i\in\mathcal{V}} w_i \cdot h_i, \quad w_i = \frac{\eta_{K,i}}{\sum_j \eta_{K,j}}
+    \end{equation}
+    误差越大的节点对全局上下文的贡献越大
+  \item \textbf{注意力门控广播：}将 $g$ 广播回每个节点，通过可学习的注意力门控 $\gamma_i \in [0,1]$ 控制每个节点对全局信息的接收程度：
+    \begin{equation}
+      h_i' = h_i + \gamma_i \cdot g, \quad \gamma_i = \sigma\big(\mathrm{MLP}([h_i, g])\big)
+    \end{equation}
+    不同物理区域的节点对全局信息的需求不同：介质界面附近需要远场上下文，均匀介质内部几乎不需要
+\end{enumerate}
+
+\textbf{GNN 总参数量：}92,740
+
+\subsubsection{Actor-Critic 双头}
+
+\begin{itemize}
+  \item \textbf{策略头（Actor）：}MLP(64, 32) + Tanh $\to$ Linear(32, 1) $\to$ 动作均值 $\mu_i$；可学习 log\_std（初始化 $-2.0$，截断 $[-4.0, -1.0]$）$\to$ \texttt{DiagGaussianDistribution}
+  \item \textbf{价值头（Critic）：}MLP(64, 32) + Tanh $\to$ Linear(32, 1) $\to$ 逐元素价值 $V_i$
+  \item 策略头和价值头不共享除 GNN backbone 外的参数
+\end{itemize}
+
+\subsection{PPO 训练}
+
+\subsubsection{处理可变智能体数量}
+
+网格细化导致元素数量变化，标准 RL 假设固定数量 agent。解决方案：在 GAE 计算阶段，通过 \texttt{scatter\_add} 将子节点价值 $V_j(s_{t+1})$ 按 \texttt{agent\_mapping} $\phi_{ij}$ 投影回父节点索引：
+
+\begin{equation}
+  \delta_i^t = r_i(s_t, a_t) + \gamma \cdot \sum_{j} \phi_{ij}^t \cdot V_j(s_{t+1}) - V_i(s_t)
+\end{equation}
+
+\subsubsection{训练超参数}
+
+\begin{table}[h]
+\centering
+\begin{tabular}{ll}
+\toprule
+参数 & 值 \\
+\midrule
+Rollout 步数 & 256 / iteration \\
+PPO epochs & 3 / iteration \\
+折扣因子 $\gamma$ & 0.99 \\
+GAE $\lambda$ & 0.95 \\
+Clip range & 0.2 \\
+Max grad norm & 0.5 \\
+学习率 & $3\times10^{-4}$（Adam） \\
+熵系数 & 0.005 \\
+价值损失系数 & 0.5 \\
+总迭代数 & 401 \\
+\bottomrule
+\end{tabular}
+\end{table}
+
+\subsection{动作掩码：Reverse D\"{o}rfler}
+
+在动作选择前，应用"反向 D\"{o}rfler"过滤：按 $\eta_K$ 升序排列单元，累计误差贡献 $< 1\%$ 总误差能量的尾部单元被标记为不可细化（排除数值噪声）。同时设 20\% 最低可选比例，确保智能体始终有充足的选择空间。
+
+% ============================================================
+\section{Experiments（实验）}
+% ============================================================
+
+\textbf{标注说明：}红色标注 \needexp{...} 表示尚未完成的实验。
+
+\subsection{实验设置}
+
+\begin{itemize}
+  \item \textbf{PDE 求解器：}scikit-fem, P1 三角单元
+  \item \textbf{计算域：}$[0,1]^2$，默认散射体为圆形介质柱
+  \item \textbf{训练 PDE 分布：}$k \in [3, 15]$ 随机采样，$\varepsilon_r \in [2.0, 4.0]$ 随机采样，圆形散射体半径和位置随机
+  \item \textbf{初始网格：}密度 $\propto k^2$，预渐近约束 $h \leq \lambda_d/1.5$
+  \item \textbf{训练配置：}401 iteration $\times$ 256 rollout steps，单 GPU 约 55 分钟
+  \item \textbf{硬件：}[填写 GPU 型号]
+\end{itemize}
+
+\subsection{基线方法}
+
+\begin{enumerate}[leftmargin=*]
+  \item \textbf{均匀细化（Uniform）：}每步对所有单元无差别细化（等价于全局 $h$-refinement）
+  \item \textbf{D\"{o}rfler 标记（D\"{o}rfler）：}使用 $\eta_K$ 作为误差指示子，D\"{o}rfler 参数 $\theta=0.5$，标记累计误差占比 $\geq 50\%$ 的最小单元集合
+  \item \textbf{最大策略标记（Max-marking）：}每步选取 $\eta_K$ 最高的 top-$k$ 单元（$k$ 与 RL 预算一致）
+  \item \textbf{随机策略（Random）：}在可选单元中等概率随机选择
+  \item \textbf{RL w/o GVN（消融）：}本文方法的 GVN 消融变体
+\end{enumerate}
+
+\subsection{主要结果}
+
+\subsubsection{误差-自由度曲线（Error vs.\ DOF）}
+
+\needexp{在 $k=10, 15, 20, 25, 30$ 下，绘制 RL 策略与所有基线的 error vs.\ DOF 曲线。每条曲线 4--6 个细化步。}
+
+\begin{itemize}
+  \item \textbf{预期结果：}RL 策略在所有波数下位于所有基线曲线之下（同等 DOF 误差更小，或同等误差更省计算）
+  \item \textbf{评估指标：}$\ell_2$ 相对误差（vs Mie 解析解或超精细参考解），全局 $\eta_K$ 总和
+  \item \textbf{表格：}列出各方法在不同波数 $k$ 和不同细化步下的 $\ell_2$ 误差与单元数
+\end{itemize}
+
+\subsubsection{跨波数零样本泛化}
+
+\needexp{训练集 $k\in[3,15]$，测试集 $k=20, 25, 30, 35$。绘制 error vs.\ DOF 曲线，对比 RL 策略与 D\"{o}rfler 标记在未见波数下的表现。}
+
+这是区分本文方法与所有传统 AMR 方法的核心实验：
+\begin{itemize}
+  \item D\"{o}rfler 参数 $\theta$ 固定为 0.5（在 $k=15$ 调优）——预期在高 $k$ 下性能退化
+  \item RL 策略不做任何调整——预期在 $k=30$ 下仍保持甚至扩大优势
+  \item 如果 RL 在 $k=30$ 的 error-vs-DOF 仍优于 D\"{o}rfler，直接证明 $k$ 不变特征的有效性
+\end{itemize}
+
+\subsubsection{跨几何泛化}
+
+\needexp{训练全部用圆形散射体。测试：方形介质柱、双圆柱、三圆柱。展示 error vs.\ DOF 曲线和网格快照。}
+
+\subsubsection{跨介质参数泛化}
+
+\needexp{训练集 $\varepsilon_r\in[2,4]$，测试 $\varepsilon_r=6,8$。展示 error vs.\ DOF。}
+
+\subsubsection{网格演化可视化}
+
+\needexp{选取代表性 case（$k=20$，方形散射体），展示 RL 策略从初始网格到最终网格的逐步细化快照，与 D\"{o}rfler 标记的对应步快照并列对比。}
+
+预期观察：RL 策略在介质界面和高梯度区域集中细化，在均匀区域保持粗网格；D\"{o}rfler 标记可能在远离界面的区域"浪费"细化预算。
+
+\subsection{消融实验}
+
+\subsubsection{GVN 消融}
+
+\needexp{训练两个模型：完整 RL（含 GVN）vs RL w/o GVN（仅 2 层 message passing）。在 $k=10, 20, 30$ 下对比 error vs.\ DOF。}
+
+\textbf{核心假设：}
+\begin{itemize}
+  \item 低 $k$（$k=10$）：GVN 和 w/o GVN 表现接近（误差传播范围小，局部信息足够）
+  \item 高 $k$（$k=30$）：GVN 显著优于 w/o GVN（非局域误差传播范围扩大，需要全局上下文）
+  \item 交互效应：$k$ 越高，GVN 的增益越大——这直接证明 GVN 解决了非局域误差传播问题
+\end{itemize}
+
+\subsubsection{零和奖励消融}
+
+\needexp{RL w/ zero-sum vs RL w/o zero-sum，对比训练曲线和最终 error vs.\ DOF。}
+
+\subsubsection{$k$ 不变特征消融}
+
+\needexp{三组对比：
+(a) 完整 13 维节点特征 + 相位距离边特征
+(b) 移除 cos/sin 相位特征（节点特征 -2 维）
+(c) 相位距离边特征 → 普通欧氏距离边特征}
+测试跨波数泛化性能差异。
+
+\subsubsection{消息传递层数消融}
+
+\needexp{1 层 vs 2 层 vs 3 层 message passing stack，对比训练收敛速度和最终性能。}
+
+\subsection{训练诊断与分析}
+
+以下数据可从前 401 次迭代的训练日志直接提取（\textbf{无需额外实验}）：
+
+\begin{itemize}
+  \item \textbf{学习曲线：}loss、explained variance、平均奖励、neg\_action\_ratio 随 iteration 的演化（附 4 合 1 图）
+  \item \textbf{neg\_action\_ratio 分析：}从 0.79（几乎所有单元都想细化）收敛到 0.05（高度选择性），解释策略如何学到"精细化是稀缺资源"
+  \item \textbf{Explained variance 分析：}从 $-0.007$（比随机还差）到 0.48（可靠的回报预测），说明价值网络学到了有意义的误差分布
+  \item \textbf{动作分布统计：}不同训练阶段策略输出 $x_i$ 的分布变化
+  \item \textbf{Mie 解验证：}\needexp{FEM 解 vs Mie 级数解析解在远场的相对 $\ell_2$ 误差，作为 FEM 求解器本身的精度基准}
+\end{itemize}
+
+% ============================================================
+\section{Discussion（讨论）}
+% ============================================================
+
+\subsection{核心发现}
+
+\begin{itemize}
+  \item \textbf{RL 策略学到了超越 D\"{o}rfler 的细化模式：}传统 D\"{o}rfler 标记是单步贪心的——每步独立标记累计误差占比 $\geq \theta$ 的最小集合。RL 策略可以在早期步骤保留预算，在后期步骤集中处理高价值区域，实现跨步优化
+  \item \textbf{GVN 解决了亥姆霍兹非局域性的信息瓶颈：}GVN 消融在高 $k$ 下的显著退化证明了全局上下文对高频波问题的重要性。这为未来将 RL-AMR 应用于其他非局域 PDE（如积分-微分方程、分数阶方程）提供了架构参考
+  \item \textbf{$k$ 不变特征是跨波数泛化的关键：}策略无需在高频下重新训练或调参——这是传统 AMR 方法无法做到的，体现了 ML 方法的核心优势
+  \item \textbf{$\eta_K$ 作为 reward 使方法具有实用性：}不依赖解析解或超精细参考网格，原则上可应用于任意复杂介质分布
+\end{itemize}
+
+\subsection{局限性}
+
+\begin{itemize}
+  \item \textbf{仅限 2D 亥姆霍兹：}拓展到 3D Maxwell 或弹性波方程需要处理更大的图规模（网格节点数 $\propto k^3$），GNN 的计算效率将成为瓶颈
+  \item \textbf{P1 单元的固有色散误差未被修正：}当前方法通过 $h$-refinement 间接补偿 P1 的色散缺陷，而非从变分形式层面消除。在高 $k$ 极限下，细化成本不可持续
+  \item \textbf{训练仍需 PDE 求解器交互：}每步 rollout 需要一次 FEM 求解，训练成本与 PDE 求解开销线性相关。离线预训练或迁移学习可缓解
+  \item \textbf{$\eta_K$ 在预渐近区的可靠性依赖于约束：}当初始网格严重欠分辨时（$h \gg \lambda$），$\eta_K$ 的可靠性退化。预渐近约束是一种缓解但非根本解决
+\end{itemize}
+
+\subsection{未来方向}
+
+\subsubsection{双加权残差（DWR）：引入因果律}
+
+当前 $\eta_K$ 仅衡量局部残差大小，不区分残差的"重要性"。DWR 理论通过求解伴随问题获得误差的因果权重：
+\begin{equation}
+  J(e) = \sum_{K\in\Omega_h} \Big(\langle r_{\mathrm{int}}, z-z_h\rangle_K + \langle r_{\mathrm{jump}}, z-z_h\rangle_{\partial K}\Big)
+\end{equation}
+将伴随解 $z_h$ 的梯度作为 GNN 的额外节点特征，网络可以直接"看到"哪些局部残差对关心的目标泛函（如远场散射截面）有实质性贡献。这是从"盲目的局部残差驱动"向"因果律驱动的物理感知"的关键一步。
+
+\subsubsection{相空间方法（Wigner 分布）：动量解耦}
+
+在含横向动量的复杂散射中，空间域标量残差掩盖了误差的物理本质——污染效应的根源是波矢方向的失配。将波场映射到位置-动量相空间（Wigner 分布），以动量偏差作为奖励信号，智能体优化目标从"缩小数值差异"升级为"逼近真实的物理色散关系"。
+
+\subsubsection{算子层面修正（GLS / Trefftz 方法）}
+
+从变分形式出发，通过 Galerkin Least-Squares (GLS) 稳定化或 Trefftz 基函数（平面波非连续 Galerkin）在 FEM 层面消除色散误差，使 GNN 面对的是干净、局域化的残差场，而非被污染效应扭曲的误差分布。
+
+% ============================================================
+\section{Conclusion（结论）}
+% ============================================================
+
+\begin{itemize}
+  \item \textbf{贡献：}将 RL-AMR 首次拓展到高频亥姆霍兹散射问题，通过 GVN 架构解决非局域误差传播，通过 $k$ 不变特征实现跨波数零样本泛化，通过 $\eta_K$ 奖励信号使方法独立于解析解
+  \item \textbf{关键证据：}[待实验完成后填写：在 $k=30$ 下 RL 策略的 error vs.\ DOF 优于 D\"{o}rfler 标记 XX\%，GVN 在高波数下贡献 YY\%]
+  \item \textbf{影响：}为高频波传播问题的数据驱动网格优化提供了新范式，GVN 架构对非局域 PDE 的 RL-AMR 具有通用参考价值
+  \item \textbf{边界：}当前框架适用于 2D Helmholtz 散射问题，在预渐近约束满足的条件下效果最佳
+\end{itemize}
+
+% ============================================================
+% 附录：实验清单
+% ============================================================
+\clearpage
+\section*{附录 A：待完成实验清单}
+
+以下所有实验需要在投稿前完成。按优先级排列。
+
+\begin{table}[h]
+\centering
+\begin{tabular}{p{0.7cm} p{5cm} p{4cm} p{4cm}}
+\toprule
+优先级 & 实验 & 支撑的创新点 & 预计工作量 \\
+\midrule
+P0 & $k=10,15,20,25,30$ 下 Error vs.\ DOF（5种方法 $\times$ 5波数 $\times$ 4-6步） & C1, C2 & 2--3 天 GPU 计算 \\
+\hline
+P0 & 跨波数泛化：训练 $k\in[3,15]$，测试 $k=20,25,30,35$ & C2（核心卖点）& 1--2 天 GPU \\
+\hline
+P0 & GVN 消融：w/ vs w/o GVN @ $k=10,20,30$ & C1 & 1 天 GPU \\
+\hline
+P1 & 跨几何泛化：方形、多圆柱测试 & C1 的几何稳健性 & 1 天 GPU \\
+\hline
+P1 & 零和奖励消融 & C4 的奖励设计贡献 & 0.5 天 GPU \\
+\hline
+P1 & 网格演化可视化对比（RL vs D\"{o}rfler）& C1 的定性证据 & 0.5 天脚本 \\
+\hline
+P2 & 跨介质 $\varepsilon_r$ 泛化 & 特征设计的稳健性 & 1 天 GPU \\
+\hline
+P2 & $k$ 不变特征消融（去相位特征/换欧氏距离）& C2 的机制解释 & 1 天 GPU \\
+\hline
+P2 & 消息传递层数消融 & 架构设计的合理性 & 0.5 天 GPU \\
+\hline
+P3 & Mie 解定量对比 & FEM 求解器精度基准 & 0.5 天脚本 \\
+\hline
+\end{tabular}
+\end{table}
+
+\vspace{1em}
+\textbf{预计总 GPU 计算时间：}8--12 天（部分可并行）。
+
+\end{document}
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diff --git a/src/config.yaml b/src/config.yaml
index aa462ad..18c0de0 100644
--- a/src/config.yaml
+++ b/src/config.yaml
@@ -8,6 +8,12 @@
 # 可视化：
 # python src/main.py --mode viz --checkpoint checkpoints/model_iter0400.pt
 # python src/main.py --mode viz --checkpoint checkpoints/model_iter0100.pt --k-test 8.0 --center 0.6,0.5 --radius 0.1
+#
+#
+# sbatch方式：
+# 训练
+# sbatch sbatch_train.sh
+#
 ###########################
 
 algorithm:
@@ -15,8 +21,8 @@ algorithm:
     discount_factor: 1.0
     ppo:
         clip_range: 0.2
-        entropy_coefficient: 0.001
-        epochs_per_iteration: 5 # 每轮迭代对同一批 rollout 数据重复训练几个 epoch
+        entropy_coefficient: 0.005
+        epochs_per_iteration: 3 # 每轮迭代对同一批 rollout 数据重复训练几个 epoch
         gae_lambda: 0.95
         initial_log_std: -2.0 # 初始动作 log 标准差，exp(-2)≈0.135
         max_grad_norm: 0.5
@@ -34,7 +40,7 @@ environment:
             solution_std: true
             timestep: true
             volume: true
-            wave_number: true
+            wave_number: false
             x_position: false
             y_position: false
             dist_to_interface: true
@@ -47,33 +53,33 @@ environment:
                 boundary:
                     - 0
                     - 0
-                    - 3
-                    - 3
-                initial_num_elements: 75
+                    - 1
+                    - 1
+                initial_num_elements: 65
             helmholtz:
                 k_ref: 6.0
                 k_exponent: 2.0
                 scatterer:
-                    cx: 1.5
+                    cx: 0.5
                     cx_max: 0.8
                     cx_min: 0.2
-                    cy: 1.5
+                    cy: 0.5
                     cy_max: 0.8
                     cy_min: 0.2
-                    eps_r: 5.0
+                    eps_r: 10.0
                     eps_r_max: 8.0
                     eps_r_min: 2.0
                     mode: random_uniform
-                    radius: 0.2
+                    radius: 0.1
                     radius_max: 0.2
                     radius_min: 0.05
                 wave_number: 30.0
-                wave_number_max: 3.0
-                wave_number_min: 15.0
+                wave_number_max: 15.0
+                wave_number_min: 3.0
                 wave_number_mode: random_uniform
             num_pdes: 100
             pde_type: helmholtz
-            pre_asymptotic_N: 1.5
+            pre_asymptotic_N: 2.0
         maximum_elements: 50000
         num_timesteps: 4
         refinement_strategy: continuous_sizing_field
@@ -104,5 +110,5 @@ network:
     latent_dimension: 64
     training:
         learning_rate: 0.0003
-        lr_decay: 0.995
+        lr_decay: 1
         optimizer: adam
diff --git a/src/helmholtz_alt.py b/src/helmholtz_alt.py
new file mode 100644
index 0000000..52c6d96
--- /dev/null
+++ b/src/helmholtz_alt.py
@@ -0,0 +1,264 @@
+"""Alternative scatterer geometries for Helmholtz FEM problems.
+
+Supports non-circular dielectric scatterers: square, multiple circles, etc.
+Each class overrides only the geometry-dependent methods of HelmholtzProblem.
+"""
+
+from typing import Any, Dict, Union
+
+import numpy as np
+from skfem import Mesh
+
+from environment.helmholtz import (
+    HelmholtzProblem,
+    _compute_residual_indicator,
+)
+
+
+# ═══════════════════════════════════════════════════════════════════
+#  Square dielectric scatterer
+# ═══════════════════════════════════════════════════════════════════
+
+class HelmholtzProblemSquare(HelmholtzProblem):
+    """Helmholtz problem with a square dielectric scatterer.
+
+    Extra config keys under helmholtz.scatterer.square:
+        half_side: float  — half side length (default 0.2)
+        angle: float      — rotation in radians (default 0.0)
+    """
+
+    def __init__(
+        self,
+        *,
+        fem_config: Dict[Union[str, int], Any],
+        random_state: np.random.RandomState = np.random.RandomState(),
+    ):
+        sc = fem_config.get("helmholtz", {}).get("scatterer", {})
+        sq = sc.get("square", {})
+        self._sq_cx = float(sq.get("cx", sc.get("cx", 0.5)))
+        self._sq_cy = float(sq.get("cy", sc.get("cy", 0.5)))
+        self._sq_half = float(sq.get("half_side", sc.get("radius", 0.2)))
+        self._sq_angle = float(sq.get("angle", 0.0))
+        self._sq_eps_r = float(sc.get("eps_r", 2.0))
+
+        super().__init__(fem_config=fem_config, random_state=random_state)
+        self._eps_r = self._sq_eps_r
+
+    # ── geometry helpers ──
+
+    def _rotate_xy(self, x, y):
+        """Rotate coordinates back to scatterer-local frame."""
+        if self._sq_angle == 0:
+            return x - self._sq_cx, y - self._sq_cy
+        c, s = np.cos(-self._sq_angle), np.sin(-self._sq_angle)
+        dx, dy = x - self._sq_cx, y - self._sq_cy
+        return c * dx - s * dy, s * dx + c * dy
+
+    def _in_square(self, x, y):
+        xr, yr = self._rotate_xy(x, y)
+        return (np.abs(xr) <= self._sq_half) & (np.abs(yr) <= self._sq_half)
+
+    # ── FEM assembly (called at quadrature points) ──
+
+    def _eps_r_at_quad_points(self, x, y):
+        return np.where(self._in_square(x, y), self._sq_eps_r, 1.0)
+
+    # ── midpoint eps_r for error estimation / features ──
+
+    def eps_r_at_midpoints(self, mesh: Mesh) -> np.ndarray:
+        pts = np.mean(mesh.p[:, mesh.t], axis=1).T
+        return np.where(self._in_square(pts[:, 0], pts[:, 1]), self._sq_eps_r, 1.0)
+
+    # ── override error estimation ──
+
+    def get_error_estimate_per_element(self, basis, solution):
+        eps_r_arr = self.eps_r_at_midpoints(basis.mesh)
+        return {"indicator": _compute_residual_indicator(
+            basis.mesh, solution, k=self._k, eps_r=eps_r_arr)}
+
+    # ── override features ──
+
+    def element_features(self, mesh, element_feature_names):
+        features_list = []
+        if "epsilon_r" in element_feature_names:
+            features_list.append(self.eps_r_at_midpoints(mesh)[:, None])
+        return np.concatenate(features_list, axis=1) if features_list else None
+
+    # ── Nyquist enforcement uses square bounding box ──
+
+    def _enforce_nyquist_in_dielectric(self, mesh, N=1.5, max_iter=10):
+        lambda_d = 2.0 * np.pi / (self._k * np.sqrt(self._sq_eps_r))
+        h_max = lambda_d / N
+
+        for _ in range(max_iter):
+            i0, i1, i2 = mesh.t[0], mesh.t[1], mesh.t[2]
+            x0, y0 = mesh.p[0, i0], mesh.p[1, i0]
+            x1, y1 = mesh.p[0, i1], mesh.p[1, i1]
+            x2, y2 = mesh.p[0, i2], mesh.p[1, i2]
+
+            e01 = np.sqrt((x1 - x0) ** 2 + (y1 - y0) ** 2)
+            e12 = np.sqrt((x2 - x1) ** 2 + (y2 - y1) ** 2)
+            e20 = np.sqrt((x0 - x2) ** 2 + (y0 - y2) ** 2)
+            h_K = np.maximum(np.maximum(e01, e12), e20)
+
+            midpoints = np.mean(mesh.p[:, mesh.t], axis=1).T
+            in_dielectric = self._in_square(midpoints[:, 0], midpoints[:, 1])
+            to_refine = np.where(in_dielectric & (h_K > h_max))[0]
+            if len(to_refine) == 0:
+                break
+            mesh = mesh.refined(to_refine)
+        return mesh
+
+    # ── visualization overlay ──
+
+    def additional_plots_from_mesh(self, mesh: Mesh) -> Dict:
+        corners = np.array([
+            [-self._sq_half, -self._sq_half],
+            [ self._sq_half, -self._sq_half],
+            [ self._sq_half,  self._sq_half],
+            [-self._sq_half,  self._sq_half],
+            [-self._sq_half, -self._sq_half],
+        ])
+        if self._sq_angle != 0:
+            c, s = np.cos(self._sq_angle), np.sin(self._sq_angle)
+            rot = np.array([[c, -s], [s, c]])
+            corners = corners @ rot.T
+        corners[:, 0] += self._sq_cx
+        corners[:, 1] += self._sq_cy
+        return {"square_outline": (corners[:, 0], corners[:, 1])}
+
+
+# ═══════════════════════════════════════════════════════════════════
+#  Multi-circle dielectric scatterer
+# ═══════════════════════════════════════════════════════════════════
+
+class HelmholtzProblemMultiCircle(HelmholtzProblem):
+    """Helmholtz problem with multiple circular dielectric scatterers.
+
+    Extra config key under helmholtz.scatterer:
+        circles: list of dicts, each with cx, cy, radius, eps_r
+    """
+
+    def __init__(
+        self,
+        *,
+        fem_config: Dict[Union[str, int], Any],
+        random_state: np.random.RandomState = np.random.RandomState(),
+    ):
+        sc = fem_config.get("helmholtz", {}).get("scatterer", {})
+        circles_cfg = sc.get("circles", None)
+        if circles_cfg is None:
+            circles_cfg = [{
+                "cx": sc.get("cx", 0.35), "cy": sc.get("cy", 0.35),
+                "radius": sc.get("radius", 0.12), "eps_r": sc.get("eps_r", 3.0),
+            }, {
+                "cx": sc.get("cx", 0.65) if "cx2" not in sc else sc["cx2"], "cy": sc.get("cy", 0.65) if "cy2" not in sc else sc["cy2"],
+                "radius": sc.get("radius", 0.12), "eps_r": sc.get("eps_r", 3.0),
+            }]
+
+        self._circles = []
+        for c in circles_cfg:
+            self._circles.append({
+                "cx": float(c["cx"]),
+                "cy": float(c["cy"]),
+                "radius": float(c["radius"]),
+                "eps_r": float(c.get("eps_r", 2.0)),
+            })
+
+        super().__init__(fem_config=fem_config, random_state=random_state)
+        sc_primary = self._circles[0]
+        self._eps_r = sc_primary["eps_r"]
+        self._cx = sc_primary["cx"]
+        self._cy = sc_primary["cy"]
+        self._radius = sc_primary["radius"]
+
+    # ── geometry ──
+
+    def _eps_r_at_point(self, x, y):
+        """Return eps_r at arbitrary points (broadcast-safe)."""
+        out = np.ones_like(x, dtype=float)
+        for c in self._circles:
+            in_c = (x - c["cx"]) ** 2 + (y - c["cy"]) ** 2 <= c["radius"] ** 2
+            out = np.where(in_c, c["eps_r"], out)
+        return out
+
+    # ── FEM assembly ──
+
+    def _eps_r_at_quad_points(self, x, y):
+        return self._eps_r_at_point(x, y)
+
+    # ── midpoint eps_r ──
+
+    def eps_r_at_midpoints(self, mesh: Mesh) -> np.ndarray:
+        pts = np.mean(mesh.p[:, mesh.t], axis=1).T
+        return self._eps_r_at_point(pts[:, 0], pts[:, 1])
+
+    # ── error estimation ──
+
+    def get_error_estimate_per_element(self, basis, solution):
+        eps_r_arr = self.eps_r_at_midpoints(basis.mesh)
+        return {"indicator": _compute_residual_indicator(
+            basis.mesh, solution, k=self._k, eps_r=eps_r_arr)}
+
+    # ── features ──
+
+    def element_features(self, mesh, element_feature_names):
+        features_list = []
+        if "epsilon_r" in element_feature_names:
+            features_list.append(self.eps_r_at_midpoints(mesh)[:, None])
+        return np.concatenate(features_list, axis=1) if features_list else None
+
+    # ── Nyquist enforcement for all circles ──
+
+    def _enforce_nyquist_in_dielectric(self, mesh, N=1.5, max_iter=15):
+        for _ in range(max_iter):
+            i0, i1, i2 = mesh.t[0], mesh.t[1], mesh.t[2]
+            x0, y0 = mesh.p[0, i0], mesh.p[1, i0]
+            x1, y1 = mesh.p[0, i1], mesh.p[1, i1]
+            x2, y2 = mesh.p[0, i2], mesh.p[1, i2]
+
+            e01 = np.sqrt((x1 - x0) ** 2 + (y1 - y0) ** 2)
+            e12 = np.sqrt((x2 - x1) ** 2 + (y2 - y1) ** 2)
+            e20 = np.sqrt((x0 - x2) ** 2 + (y0 - y2) ** 2)
+            h_K = np.maximum(np.maximum(e01, e12), e20)
+
+            midpoints = np.mean(mesh.p[:, mesh.t], axis=1).T
+            eps_r_at_mid = self._eps_r_at_point(midpoints[:, 0], midpoints[:, 1])
+            lambda_local = 2.0 * np.pi / (self._k * np.sqrt(np.maximum(eps_r_at_mid, 1.0)))
+            h_max = lambda_local / N
+
+            to_refine = np.where((eps_r_at_mid > 1.0) & (h_K > h_max))[0]
+            if len(to_refine) == 0:
+                break
+            mesh = mesh.refined(to_refine)
+        return mesh
+
+    # ── visualization overlay ──
+
+    def additional_plots_from_mesh(self, mesh: Mesh) -> Dict:
+        result = {}
+        for i, c in enumerate(self._circles):
+            theta = np.linspace(0, 2 * np.pi, 128)
+            result[f"circle_{i}"] = (
+                c["cx"] + c["radius"] * np.cos(theta),
+                c["cy"] + c["radius"] * np.sin(theta),
+            )
+        return result
+
+
+# ═══════════════════════════════════════════════════════════════════
+#  Factory functions  (mirror create_helmholtz_problem)
+# ═══════════════════════════════════════════════════════════════════
+
+def create_helmholtz_problem_square(
+    *, fem_config: Dict[Union[str, int], Any],
+    random_state: np.random.RandomState = np.random.RandomState(),
+) -> HelmholtzProblemSquare:
+    return HelmholtzProblemSquare(fem_config=fem_config, random_state=random_state)
+
+
+def create_helmholtz_problem_multi_circle(
+    *, fem_config: Dict[Union[str, int], Any],
+    random_state: np.random.RandomState = np.random.RandomState(),
+) -> HelmholtzProblemMultiCircle:
+    return HelmholtzProblemMultiCircle(fem_config=fem_config, random_state=random_state)
diff --git a/src/main.py b/src/main.py
index 3e37230..02b5921 100644
--- a/src/main.py
+++ b/src/main.py
@@ -49,6 +49,8 @@ def train(config: dict, iterations: int, checkpoint_dir: str = "checkpoints", sa
             f"agents={metrics['num_agents']:.0f} avg_r={metrics['avg_reward']:.4f} sum_r={metrics['sum_reward']:.2f} "
             f"x<0={metrics.get('neg_action_ratio', 0):.2f} "
             f"elig={metrics.get('eligible_ratio', 0):.2f} "
+            f"dorfler_tail={metrics.get('dorfler_tail_ratio', 0):.2f} "
+            f"floor={metrics.get('dorfler_floor_active', 0):.0f} "
             f"sel={metrics.get('selected_count', 0):.0f} "
             f"{time.time() - t1:.1f}s"
         )
@@ -60,7 +62,7 @@ def train(config: dict, iterations: int, checkpoint_dir: str = "checkpoints", sa
 
 
 def _eval_mie_error_test(env) -> float:
-    """Compute relative L2 error of FEM vs Mie analytical solution."""
+    """Compute relative L2 error of FEM vs Mie analytical solution (vertex-level)."""
     fp = getattr(env.fem_problem, "fem_problem", None)
     if fp is None:
         return float("nan")
@@ -83,6 +85,60 @@ def _eval_mie_error_test(env) -> float:
     return float(np.linalg.norm(diff) / denom)
 
 
+def _eval_mie_error_area_weighted(env):
+    """Compute area-weighted relative error FEM vs Mie (triangle-level quadrature).
+
+    Returns dict with keys:
+        rel_err  — area-weighted relative error (0–1)
+        w_rmse   — area-weighted RMSE
+        max_err  — max pointwise absolute error (L∞)
+    """
+    fp = getattr(env.fem_problem, "fem_problem", None)
+    if fp is None:
+        return {"rel_err": float("nan"), "w_rmse": float("nan"), "max_err": float("nan")}
+    _eps_r = getattr(fp, "_eps_r", None)
+    _radius = getattr(fp, "_radius", None)
+    _cx = getattr(fp, "_cx", None)
+    _cy = getattr(fp, "_cy", None)
+    _k = getattr(fp, "_k", None)
+    if any(v is None for v in [_eps_r, _radius, _cx, _cy, _k]):
+        return {"rel_err": float("nan"), "w_rmse": float("nan"), "max_err": float("nan")}
+
+    from environment.mie_solution import mie_scattered_field
+
+    mesh = env.mesh
+    pts = mesh.p.T               # (num_vertices, 2)
+    tri = mesh.t.T               # (num_triangles, 3) — vertex indices
+
+    u_mie = mie_scattered_field(pts, k0=_k, eps_r=_eps_r, radius=_radius, cx=_cx, cy=_cy)
+    u_fem = env.scalar_solution
+
+    err_abs = np.abs(u_fem - u_mie)
+    ref_abs = np.abs(u_mie)
+
+    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])
+    )
+
+    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
+
+    total_area = np.sum(tri_areas)
+    w_rmse = np.sqrt(np.sum(err_tri_sq * tri_areas) / total_area)
+
+    ref_total = np.sum(ref_tri_sq * tri_areas)
+    rel_err = np.sqrt(np.sum(err_tri_sq * tri_areas) / ref_total) if ref_total > 1e-12 else float("nan")
+
+    return {"rel_err": float(rel_err), "w_rmse": float(w_rmse),
+            "max_err": float(np.max(err_abs))}
+
+
 def test(config: dict, checkpoint_path: str, k_test=None, center=None, radius=None, eps_test=None):
     setup_helmholtz_config(config, k_test=k_test, center=center, radius=radius, eps_test=eps_test)
     algo = config.get("algorithm", {})
@@ -102,8 +158,11 @@ def test(config: dict, checkpoint_path: str, k_test=None, center=None, radius=No
     step = 0
     n_elem_init = getattr(env, "_num_elements", env.num_agents)
     mie_err_0 = _eval_mie_error_test(env)
-    print(f"  Step {step:2d}: reward=---      mie_err={mie_err_0:.4f}  elements={n_elem_init}"
-          f"  budget={getattr(env, '_n_budget', '?')}")
+    aw_0 = _eval_mie_error_area_weighted(env)
+    print(f"  Step {step:2d}: reward=---      mie_err={mie_err_0:.4f}  "
+          f"aw_rel={aw_0['rel_err']*100:.2f}%  aw_rmse={aw_0['w_rmse']:.4f}  "
+          f"max_err={aw_0['max_err']:.4f}  elements={n_elem_init}  "
+          f"budget={getattr(env, '_n_budget', '?')}")
 
     total_reward = 0.0
     while not done:
@@ -113,12 +172,29 @@ def test(config: dict, checkpoint_path: str, k_test=None, center=None, radius=No
         step_r = float(np.sum(reward))
         total_reward += step_r
         step += 1
-        mie_err = _eval_mie_error_test(env)
-        print(f"  Step {step:2d}: reward={step_r:+.4f} mie_err={mie_err:.4f}"
-              f"  elements={info.get('num_elements', '?')} "
-              f"x<0={info.get('neg_action_ratio', 0):.2f} sel={info.get('selected_count', 0)}")
 
-    print(f"\n[Test] total_reward={total_reward:.4f} final_mie_error={mie_err:.4f}")
+        # timing
+        _timing = env.fem_problem.last_solve_timing
+        _t_str = ""
+        if _timing is not None:
+            _t_str = (f"  [timing] K={_timing['assemble_K']*1e3:.1f}ms"
+                      f"  f={_timing['assemble_f']*1e3:.1f}ms"
+                      f"  bnd={_timing['assemble_boundary']*1e3:.1f}ms"
+                      f"  solve={_timing['solve']*1e3:.1f}ms"
+                      f"  total={_timing['total']*1e3:.1f}ms"
+                      f"  n_dof={_timing['n_dof']}")
+
+        mie_err = _eval_mie_error_test(env)
+        aw = _eval_mie_error_area_weighted(env)
+        print(f"  Step {step:2d}: reward={step_r:+.4f} mie_err={mie_err:.4f}  "
+              f"aw_rel={aw['rel_err']*100:.2f}%  aw_rmse={aw['w_rmse']:.4f}  "
+              f"max_err={aw['max_err']:.4f}  "
+              f"elements={info.get('num_elements', '?')} "
+              f"x<0={info.get('neg_action_ratio', 0):.2f} sel={info.get('selected_count', 0)}"
+              f"{_t_str}")
+
+    print(f"\n[Test] total_reward={total_reward:.4f} final_mie_error={mie_err:.4f}"
+          f"  final_aw_rel={aw['rel_err']*100:.2f}%")
 
 
 def main():
diff --git a/src/network.py b/src/network.py
index e05a186..e675594 100644
--- a/src/network.py
+++ b/src/network.py
@@ -154,10 +154,55 @@ class MessagePassingStep(nn.Module):
 
 
 # ──
-#  6. MessagePassingStack — 堆叠 N 个 Step
+#  6. GlobalVirtualNode — 注意力门控全局广播
+# ──
+class GlobalVirtualNode(nn.Module):
+    """
+    Global Virtual Node (GVN) with attention-gated broadcast.
+
+    Stage A: h_V = mean(h_v)  — global pooling (≈ Lippmann-Schwinger integral)
+    Stage B: α_v = sigmoid(W_att[h_v || h_V] + b_att)  — per-node attention gate
+             h_v ← h_v + α_v ⊙ (W_V · h_V)  — gated broadcast
+
+    Breaks the O(diameter) information bottleneck of local message passing
+    in O(1), injecting global error distribution and coherent background
+    field context into every local node.
+    """
+
+    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)
+        # Learnable scale initialized small — prevents the GVN broadcast
+        # from homogenizing node features before the local MP signal is learned.
+        self.scale = nn.Parameter(torch.tensor(0.1))
+
+    def forward(self, graph: Data):
+        # Stage A: η_K-weighted global pooling
+        # High-error regions dominate the virtual node; free-space background is
+        # naturally suppressed.  Falls back to mean if no η available.
+        if hasattr(graph, 'eta') and graph.eta is not None:
+            w = graph.eta / (graph.eta.sum() + 1e-8)          # [N], Σw = 1
+            h_V = (graph.x * w.unsqueeze(-1)).sum(dim=0, keepdim=True)  # [1, D]
+        else:
+            h_V = graph.x.mean(dim=0, keepdim=True)           # [1, D]
+
+        # Stage B: attention-gated broadcast
+        h_V_exp = h_V.expand(graph.x.shape[0], -1)      # [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)
+
+
+# ──
+#  7. MessagePassingStack — 堆叠 N 个 Step + GVN
 # ──
 class MessagePassingStack(nn.Module):
-    """Stack of multiple MessagePassingSteps with optional step repeats."""
+    """Stack of MessagePassingSteps followed by a Global Virtual Node."""
 
     def __init__(self, latent_dim: int, stack_config: dict, scatter_reducer):
         super().__init__()
@@ -169,11 +214,13 @@ class MessagePassingStack(nn.Module):
                 for _ in range(num_steps)
             ]
         )
+        self.gvn = GlobalVirtualNode(latent_dim)
 
     def forward(self, graph: Data):
         for step in self.steps:
             for _ in range(self.num_step_repeats):
                 step(graph)
+        self.gvn(graph)
 
 
 # ──
diff --git a/src/ppo.py b/src/ppo.py
index bd1d2c4..ba08f08 100644
--- a/src/ppo.py
+++ b/src/ppo.py
@@ -186,7 +186,8 @@ class PPOTrainer:
         _rho_keys = ("rho_int_mean", "rho_jump_mean", "rho_sbc_mean",
                       "w_rho_int", "w_rho_jump", "w_rho_sbc")
         rho_accum = {k: 0.0 for k in _rho_keys}
-        diag_keys = ("neg_action_ratio", "eligible_ratio", "selected_count")
+        diag_keys = ("neg_action_ratio", "eligible_ratio", "selected_count",
+                      "dorfler_tail_ratio", "dorfler_floor_active")
         diag_accum = {k: 0.0 for k in diag_keys}
         diag_steps = 0
 
@@ -257,7 +258,7 @@ class PPOTrainer:
                 torch.nn.utils.clip_grad_norm_(self.policy.parameters(), self.max_grad_norm)
                 self.policy.optimizer.step()
                 if self.policy.log_std is not None:
-                    self.policy.log_std.data.clamp_(-4.0, -1.0)
+                    self.policy.log_std.data.clamp_(-3.0, -1.0)  # σ ∈ [0.05, 0.37]
                 total_losses.append(loss.item())
 
         if self.policy.lr_scheduler is not None:
diff --git a/src/test_config.yaml b/src/test_config.yaml
new file mode 100644
index 0000000..ae32b0b
--- /dev/null
+++ b/src/test_config.yaml
@@ -0,0 +1,53 @@
+# Test configuration for test_media.py
+# Usage: python src/test_media.py                           (uses this file by default)
+#        python src/test_media.py --k-test 8.0              (CLI overrides)
+#        python src/test_media.py --config my_test.yaml     (use a different config)
+
+# Path to base config (model/network/algo params)
+base_config: src/config.yaml
+
+# ── Test scenario ──
+test:
+  geometry: square          # square | multi_circle | circle
+  checkpoint: checkpoints/model_final.pt
+  output: result/test_square.png
+  seed: 99
+
+# ── Wave number ──
+k_test: 18.0
+
+# ── Scatterer parameters ──
+# Used based on test.geometry. Comment/uncomment as needed.
+scatterer:
+  eps_r: 3.0
+
+  # Shared position
+  cx: 0.5
+  cy: 0.5
+
+  # Circle
+  radius: 0.15
+
+  # Square
+  half_side: 0.15
+  angle: 0.0
+
+  # Multi-circle (overrides cx/cy/radius above when geometry=multi_circle)
+  circles:
+    - cx: 0.35
+      cy: 0.5
+      radius: 0.12
+      eps_r: 3.0
+    - cx: 0.65
+      cy: 0.5
+      radius: 0.12
+      eps_r: 3.0
+
+# ── Reference computation ──
+# n_refine_vertex: uniform refinement levels for per-vertex error
+# n_refine_grid:   uniform refinement levels for the 2D heatmap
+# grid_resolution: N x N grid points for the heatmap
+reference:
+  n_refine_vertex: 2
+  n_refine_grid: 3
+  grid_resolution: 200
diff --git a/src/test_media.py b/src/test_media.py
new file mode 100644
index 0000000..66894bc
--- /dev/null
+++ b/src/test_media.py
@@ -0,0 +1,609 @@
+#!/usr/bin/env python3
+"""Test a trained AFEM model on alternative scatterer geometries.
+
+Supports: square, multi-circle, and the original circle.
+
+Usage:
+    python src/test_media.py                          # uses src/test_config.yaml
+    python src/test_media.py --k-test 30.0 --geometry circle
+    python src/test_media.py --config my_test.yaml    # custom config
+
+All test parameters live in the YAML config. CLI args serve as overrides.
+"""
+
+import argparse
+import copy
+import os
+import sys
+import time
+from pathlib import Path
+from typing import Optional
+
+import numpy as np
+import torch
+from torch_geometric.data import Batch
+
+_project_root = Path(__file__).resolve().parent.parent
+if str(_project_root) not in sys.path:
+    sys.path.insert(0, str(_project_root))
+
+from src.network import create_model
+from src.utils import load_checkpoint, load_config, setup_helmholtz_config
+from src.helmholtz_alt import (
+    HelmholtzProblemSquare,
+    HelmholtzProblemMultiCircle,
+    create_helmholtz_problem_square,
+    create_helmholtz_problem_multi_circle,
+)
+
+
+# ═══════════════════════════════════════════════════════════════════════
+#  Geometry factory mapping
+# ═══════════════════════════════════════════════════════════════════════
+
+_GEOMETRY_FACTORIES = {
+    "square": create_helmholtz_problem_square,
+    "multi_circle": create_helmholtz_problem_multi_circle,
+    "circle": None,  # default HelmholtzProblem
+}
+
+
+# ═══════════════════════════════════════════════════════════════════════
+#  Epsilon_r property patching
+# ═══════════════════════════════════════════════════════════════════════
+
+def _patch_epsilon_r(env):
+    inner_fp = env.fem_problem.fem_problem
+    if hasattr(inner_fp, "eps_r_at_midpoints"):
+        def _eps_r(self):
+            return inner_fp.eps_r_at_midpoints(self.mesh)
+        type(env)._epsilon_r_elements = property(_eps_r)
+
+
+# ═══════════════════════════════════════════════════════════════════════
+#  Fine FEM reference (computed once, interpolated later)
+# ═══════════════════════════════════════════════════════════════════════
+
+def _compute_fine_fem_reference(env, n_refine: int = 2):
+    """Compute fine-FEM reference on initial mesh + n_refine uniform refinement."""
+    from skfem import Basis, ElementTriP1
+
+    fp = env.fem_problem.fem_problem
+    ref_mesh = copy.deepcopy(env.mesh)
+    for _ in range(n_refine):
+        ref_mesh = ref_mesh.refined(np.arange(ref_mesh.t.shape[1]))
+    ref_basis = Basis(ref_mesh, ElementTriP1())
+    ref_sol = fp.calculate_solution(ref_basis, cache=False)
+
+    # Interpolate to coarse mesh vertices
+    pts = env.mesh.p.T
+    finder = ref_mesh.element_finder()
+    cells = finder(*pts.T)
+    cells = np.clip(cells, 0, ref_mesh.t.shape[1] - 1)
+
+    i0, i1, i2 = ref_mesh.t[0, cells], ref_mesh.t[1, cells], ref_mesh.t[2, cells]
+    p = ref_mesh.p
+    x, y = pts[:, 0], pts[:, 1]
+    x0, y0 = p[0, i0], p[1, i0]
+    x1, y1 = p[0, i1], p[1, i1]
+    x2, y2 = p[0, i2], p[1, i2]
+    denom = (x1 - x0) * (y2 - y0) - (x2 - x0) * (y1 - y0)
+    denom = np.where(np.abs(denom) < 1e-15, 1.0, denom)
+    w0 = ((x1 - x) * (y2 - y) - (x2 - x) * (y1 - y)) / denom
+    w1 = ((x2 - x) * (y0 - y) - (x0 - x) * (y2 - y)) / denom
+    w2 = 1.0 - w0 - w1
+    u_ref_on_coarse = w0 * ref_sol[i0] + w1 * ref_sol[i1] + w2 * ref_sol[i2]
+    return u_ref_on_coarse, ref_mesh, ref_sol
+
+
+def _interpolate_ref_to_mesh(target_pts, ref_mesh, ref_sol):
+    """Interpolate cached reference solution to arbitrary mesh vertices."""
+    finder = ref_mesh.element_finder()
+    cells = finder(*target_pts.T)
+    cells = np.clip(cells, 0, ref_mesh.t.shape[1] - 1)
+
+    i0, i1, i2 = ref_mesh.t[0, cells], ref_mesh.t[1, cells], ref_mesh.t[2, cells]
+    p = ref_mesh.p
+    x, y = target_pts[:, 0], target_pts[:, 1]
+    x0, y0 = p[0, i0], p[1, i0]
+    x1, y1 = p[0, i1], p[1, i1]
+    x2, y2 = p[0, i2], p[1, i2]
+    denom = (x1 - x0) * (y2 - y0) - (x2 - x0) * (y1 - y0)
+    denom = np.where(np.abs(denom) < 1e-15, 1.0, denom)
+    w0 = ((x1 - x) * (y2 - y) - (x2 - x) * (y1 - y)) / denom
+    w1 = ((x2 - x) * (y0 - y) - (x0 - x) * (y2 - y)) / denom
+    w2 = 1.0 - w0 - w1
+    return w0 * ref_sol[i0] + w1 * ref_sol[i1] + w2 * ref_sol[i2]
+
+
+def _compute_ref_grid(env, n_refine: int = 3, resolution: int = 200):
+    """Compute fine reference on a regular grid for smooth heatmaps."""
+    from skfem import Basis, ElementTriP1
+
+    fp = env.fem_problem.fem_problem
+    ref_mesh = copy.deepcopy(env.mesh)
+    for _ in range(n_refine):
+        ref_mesh = ref_mesh.refined(np.arange(ref_mesh.t.shape[1]))
+    ref_basis = Basis(ref_mesh, ElementTriP1())
+    ref_sol = fp.calculate_solution(ref_basis, cache=False)
+
+    boundary = fp._domain._boundary
+    x_vec = np.linspace(boundary[0], boundary[2], resolution)
+    y_vec = np.linspace(boundary[1], boundary[3], resolution)
+    X, Y = np.meshgrid(x_vec, y_vec)
+    grid_pts = np.column_stack([X.ravel(), Y.ravel()])
+
+    U_grid = np.zeros(len(grid_pts), dtype=np.complex128)
+    batch_size = 4096
+    for start in range(0, len(grid_pts), batch_size):
+        end = min(start + batch_size, len(grid_pts))
+        batch = grid_pts[start:end]
+        finder = ref_mesh.element_finder()
+        cells = finder(*batch.T)
+        cells = np.clip(cells, 0, ref_mesh.t.shape[1] - 1)
+
+        i0, i1, i2 = ref_mesh.t[0, cells], ref_mesh.t[1, cells], ref_mesh.t[2, cells]
+        p = ref_mesh.p
+        x, y = batch[:, 0], batch[:, 1]
+        x0, y0 = p[0, i0], p[1, i0]
+        x1, y1 = p[0, i1], p[1, i1]
+        x2, y2 = p[0, i2], p[1, i2]
+        denom = (x1 - x0) * (y2 - y0) - (x2 - x0) * (y1 - y0)
+        denom = np.where(np.abs(denom) < 1e-15, 1.0, denom)
+        w0 = ((x1 - x) * (y2 - y) - (x2 - x) * (y1 - y)) / denom
+        w1 = ((x2 - x) * (y0 - y) - (x0 - x) * (y2 - y)) / denom
+        w2 = 1.0 - w0 - w1
+        U_grid[start:end] = w0 * ref_sol[i0] + w1 * ref_sol[i1] + w2 * ref_sol[i2]
+
+    return {"X": X, "Y": Y, "E_scat": U_grid.reshape(resolution, resolution)}
+
+
+def _compute_step_error(scalar, u_ref) -> float:
+    if u_ref is None:
+        return float("nan")
+    diff = np.abs(scalar - u_ref)
+    denom = np.linalg.norm(np.abs(u_ref))
+    if denom < 1e-12:
+        denom = 1.0
+    return float(np.linalg.norm(diff) / denom)
+
+
+# ═══════════════════════════════════════════════════════════════════════
+#  Visualization
+# ═══════════════════════════════════════════════════════════════════════
+
+def _render_field(ax, triang, values, title, vmin, vmax, show_mesh=True):
+    tcf = ax.tripcolor(triang, values, shading="gouraud", cmap="jet",
+                       vmin=vmin, vmax=vmax)
+    if show_mesh and triang is not None:
+        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_aspect("equal")
+    ax.set_title(title, fontsize=9)
+    ax.set_xticks([])
+    ax.set_yticks([])
+    return tcf
+
+
+def _draw_scatterer(ax, geometry: str, env):
+    fp = env.fem_problem.fem_problem
+    if geometry == "square":
+        sq = getattr(fp, "_sq_cx", 0.5), getattr(fp, "_sq_cy", 0.5)
+        hs = getattr(fp, "_sq_half", 0.2)
+        ang = getattr(fp, "_sq_angle", 0.0)
+        corners = np.array([
+            [-hs, -hs], [hs, -hs], [hs, hs], [-hs, hs], [-hs, -hs]
+        ])
+        if ang != 0:
+            c, s = np.cos(ang), np.sin(ang)
+            corners = corners @ np.array([[c, -s], [s, c]]).T
+        corners[:, 0] += sq[0]
+        corners[:, 1] += sq[1]
+        ax.plot(corners[:, 0], corners[:, 1], color="cyan", linewidth=1.5,
+                linestyle="--")
+    elif geometry == "multi_circle":
+        circles = getattr(fp, "_circles", [])
+        for c in circles:
+            theta = np.linspace(0, 2 * np.pi, 128)
+            ax.plot(c["cx"] + c["radius"] * np.cos(theta),
+                    c["cy"] + c["radius"] * np.sin(theta),
+                    color="cyan", linewidth=1.5, linestyle="--")
+    elif geometry == "circle":
+        cx = getattr(fp, "_cx", 0.5)
+        cy = getattr(fp, "_cy", 0.5)
+        r = getattr(fp, "_radius", 0.2)
+        theta = np.linspace(0, 2 * np.pi, 128)
+        ax.plot(cx + r * np.cos(theta), cy + r * np.sin(theta),
+                color="cyan", linewidth=1.5, linestyle="--")
+
+
+def _save_pngs(steps, stem, checkpoint_path, k, geometry, env, ref_grid):
+    import matplotlib
+    matplotlib.use("Agg")
+    import matplotlib.pyplot as plt
+    import matplotlib.tri as tri
+
+    per_step_dir = f"{stem}_steps"
+    os.makedirs(os.path.dirname(stem) or ".", exist_ok=True)
+    os.makedirs(per_step_dir, exist_ok=True)
+
+    # ── Overview grid ──
+    n = len(steps)
+    ncols = min(n, 4)
+    nrows = (n + ncols - 1) // ncols
+    fig, axes = plt.subplots(nrows, ncols, figsize=(4 * ncols, 3.5 * nrows))
+    axes_flat = np.array([axes]) if nrows * ncols == 1 else np.array(axes).flatten()
+
+    for i, step_data in enumerate(steps):
+        mesh, scalar, err_val, n_elem = step_data[:4]
+        pts = mesh.p.T
+        tg = tri.Triangulation(pts[:, 0], pts[:, 1], mesh.t.T)
+        s = np.abs(scalar) if np.iscomplexobj(scalar) else scalar
+        vmin, vmax = s.min(), s.max()
+        if vmax - vmin < 1e-12:
+            vmin, vmax = vmin - 0.5, vmax + 0.5
+        tcf = _render_field(axes_flat[i], tg, s,
+                            f"Step {i}: {n_elem} elem, err={err_val:.4f}",
+                            vmin, vmax)
+        fig.colorbar(tcf, ax=axes_flat[i], fraction=0.046, pad=0.04)
+        _draw_scatterer(axes_flat[i], geometry, env)
+
+    for j in range(n, len(axes_flat)):
+        axes_flat[j].set_visible(False)
+
+    fig.subplots_adjust(left=0.04, right=0.90, top=0.90, bottom=0.06,
+                        wspace=0.15, hspace=0.30)
+    geo_label = {"square": "Square", "multi_circle": "Multi-Circle",
+                 "circle": "Circle"}.get(geometry, geometry)
+    fig.suptitle(
+        f"Helmholtz |E_scat| [{geo_label}] — {os.path.basename(checkpoint_path)}\n"
+        f"k={k:.1f}  eps_r info in scatterer overlay",
+        fontsize=12,
+    )
+    fig.savefig(f"{stem}.png", dpi=200, bbox_inches="tight")
+    plt.close(fig)
+    print(f"[Viz] Overview → {stem}.png")
+
+    # ── Per-step panels (FEM + Reference + Error) ──
+    for i, step_data in enumerate(steps):
+        mesh, scalar, err_val, n_elem = step_data[:4]
+        u_ref_at_verts = step_data[4] if len(step_data) > 4 else None
+
+        pts = mesh.p.T
+        tg = tri.Triangulation(pts[:, 0], pts[:, 1], mesh.t.T)
+        coarse_val = np.abs(scalar) if np.iscomplexobj(scalar) else scalar
+
+        fig2, axes2 = plt.subplots(1, 3, figsize=(18, 6))
+        axes2 = list(np.atleast_1d(axes2))
+
+        # Panel 1: FEM
+        cvmin, cvmax = coarse_val.min(), coarse_val.max()
+        if cvmax - cvmin < 1e-12:
+            cvmin, cvmax = cvmin - 0.5, cvmax + 0.5
+        tcf1 = _render_field(axes2[0], tg, coarse_val,
+                             f"Step {i}: FEM |E_scat| ({n_elem} elem)",
+                             cvmin, cvmax)
+        _draw_scatterer(axes2[0], geometry, env)
+        fig2.colorbar(tcf1, ax=axes2[0], fraction=0.046, pad=0.04)
+
+        # Panel 2: Fine FEM reference on grid
+        if ref_grid is not None:
+            g = ref_grid
+            gm = np.abs(g["E_scat"])
+            mvmin, mvmax = gm.min(), gm.max()
+            if mvmax - mvmin < 1e-12:
+                mvmin, mvmax = mvmin - 0.5, mvmax + 0.5
+            im2 = axes2[1].pcolormesh(g["X"], g["Y"], gm,
+                                      shading="gouraud", cmap="jet",
+                                      vmin=mvmin, vmax=mvmax)
+            axes2[1].set_title("Fine FEM Ref |E_scat|", fontsize=9)
+            axes2[1].set_aspect("equal")
+            axes2[1].set_xticks([])
+            axes2[1].set_yticks([])
+            _draw_scatterer(axes2[1], geometry, env)
+            fig2.colorbar(im2, ax=axes2[1], fraction=0.046, pad=0.04)
+
+        # Panel 3: Pointwise error
+        if u_ref_at_verts is not None:
+            u_fem_abs = np.abs(scalar)
+            u_ref_abs = np.abs(u_ref_at_verts)
+            error_abs = np.abs(u_fem_abs - u_ref_abs)
+            evmin, evmax = 0.0, error_abs.max() or 1.0
+            if evmax - evmin < 1e-12:
+                evmax = evmin + 1.0
+            tcf3 = _render_field(axes2[2], tg, error_abs,
+                                 f"||FEM|−|Ref||  L2={err_val:.4f}",
+                                 evmin, evmax)
+            _draw_scatterer(axes2[2], geometry, env)
+            fig2.colorbar(tcf3, ax=axes2[2], fraction=0.046, pad=0.04)
+
+        fig2.tight_layout()
+        fig2.savefig(f"{per_step_dir}/step{i:02d}.png", dpi=150,
+                     bbox_inches="tight")
+        plt.close(fig2)
+
+    print(f"[Viz] Per-step PNGs → {per_step_dir}/  ({n} files)")
+
+
+# ═══════════════════════════════════════════════════════════════════════
+#  Scatterer config injection
+# ═══════════════════════════════════════════════════════════════════════
+
+def _inject_scatterer_config(base_config: dict, geometry: str, sc_cfg: dict, k_test: float):
+    """Inject scatterer params from test config into the base config's helmholtz section.
+
+    Returns (config, factory) where factory is the geometry-specific create function.
+    """
+    hc = (base_config.setdefault("environment", {})
+          .setdefault("mesh_refinement", {})
+          .setdefault("fem", {})
+          .setdefault("helmholtz", {}))
+
+    sc = hc.setdefault("scatterer", {})
+    sc["mode"] = "fixed"
+    sc["eps_r"] = float(sc_cfg.get("eps_r", 3.0))
+
+    if geometry == "square":
+        sc["square"] = {
+            "cx": float(sc_cfg.get("cx", 0.5)),
+            "cy": float(sc_cfg.get("cy", 0.5)),
+            "half_side": float(sc_cfg.get("half_side", 0.15)),
+            "angle": float(sc_cfg.get("angle", 0.0)),
+        }
+    elif geometry == "multi_circle":
+        circles_raw = sc_cfg.get("circles", [])
+        circles = []
+        for c in circles_raw:
+            circles.append({
+                "cx": float(c["cx"]), "cy": float(c["cy"]),
+                "radius": float(c["radius"]),
+                "eps_r": float(c.get("eps_r", sc_cfg.get("eps_r", 3.0))),
+            })
+        sc["circles"] = circles
+    elif geometry == "circle":
+        sc["cx"] = float(sc_cfg.get("cx", 0.5))
+        sc["cy"] = float(sc_cfg.get("cy", 0.5))
+        sc["radius"] = float(sc_cfg.get("radius", 0.2))
+
+    hc["wave_number_mode"] = "fixed"
+    hc["wave_number"] = float(k_test)
+
+    factory = _GEOMETRY_FACTORIES.get(geometry)
+    return base_config, factory
+
+
+# ═══════════════════════════════════════════════════════════════════════
+#  Main test function
+# ═══════════════════════════════════════════════════════════════════════
+
+def test_alt_media(
+    base_config: dict,
+    test_cfg: dict,
+    cli_overrides: Optional[dict] = None,
+):
+    """Run AFEM inference with config-driven parameters.
+
+    Args:
+        base_config: loaded from config.yaml (model/network/algo)
+        test_cfg: loaded from test_config.yaml (test-specific params)
+        cli_overrides: optional CLI arg overrides dict
+    """
+    ov = cli_overrides or {}
+
+    # ── Resolve parameters: test_cfg < CLI override ──
+    tc = test_cfg.get("test", {})
+    ref_cfg = test_cfg.get("reference", {})
+    sc_cfg = test_cfg.get("scatterer", {})
+
+    geometry = ov.get("geometry") or tc.get("geometry", "circle")
+    checkpoint_path = ov.get("checkpoint") or tc.get("checkpoint", "checkpoints/model_final.pt")
+    output_path = ov.get("output") or tc.get("output", "result/test_media.png")
+    seed = ov.get("seed") or tc.get("seed", 99)
+    k_test = ov.get("k_test") or test_cfg.get("k_test", 8.0)
+    n_refine_vertex = ov.get("n_refine_vertex") or ref_cfg.get("n_refine_vertex", 2)
+    n_refine_grid = ov.get("n_refine_grid") or ref_cfg.get("n_refine_grid", 3)
+    grid_resolution = ov.get("grid_resolution") or ref_cfg.get("grid_resolution", 200)
+
+    # Allow CLI override of scatterer params
+    for key in ("cx", "cy", "radius", "eps_r", "half_side", "angle"):
+        if ov.get(key) is not None:
+            sc_cfg[key] = ov[key]
+    if ov.get("circles") is not None:
+        sc_cfg["circles"] = ov["circles"]
+
+    algo = base_config.get("algorithm", {})
+
+    # ── 1. Inject scatterer config ──
+    config, factory = _inject_scatterer_config(
+        copy.deepcopy(base_config), geometry, sc_cfg, k_test)
+
+    # ── 2. Create env with alt factory ──
+    import environment.fem_problem as fem_problem_module
+
+    _orig_create = None
+    if factory is not None:
+        _orig_create = fem_problem_module.create_helmholtz_problem
+        fem_problem_module.create_helmholtz_problem = factory
+
+    from environment.mesh_refinement import MeshRefinement
+    env = MeshRefinement(
+        environment_config=config.get("environment", {}).get("mesh_refinement", {}),
+        seed=seed,
+    )
+
+    # ── 3. Load model ──
+    model = create_model(env, config.get("network", {}), algo.get("ppo", {}))
+    load_checkpoint(model, checkpoint_path)
+    model.eval()
+    dev = next(model.parameters()).device
+    print(f"[Device] {dev}")
+    model = model.to(dev)
+
+    # ── 4. Reset env ──
+    print(f"[Test] Geometry: {geometry}  k={k_test:.3f}")
+    obs = env.reset()
+
+    # ── 5. Patch epsilon_r_elements (after reset) ──
+    _patch_epsilon_r(env)
+
+    # Restore original factory
+    if _orig_create is not None:
+        fem_problem_module.create_helmholtz_problem = _orig_create
+
+    # ── 6. Print scatterer info ──
+    fp = env.fem_problem.fem_problem
+    if geometry == "square":
+        print(f"[Test]   Square: center=({getattr(fp, '_sq_cx', 0.5):.3f}, "
+              f"{getattr(fp, '_sq_cy', 0.5):.3f})  half_side={getattr(fp, '_sq_half', 0.2):.3f}")
+    elif geometry == "multi_circle":
+        circles_attr = getattr(fp, "_circles", [])
+        for i, c in enumerate(circles_attr):
+            print(f"[Test]   Circle {i}: center=({c['cx']:.3f}, {c['cy']:.3f})  "
+                  f"r={c['radius']:.3f}  eps_r={c['eps_r']:.1f}")
+    elif geometry == "circle":
+        print(f"[Test]   Circle: center=({getattr(fp, '_cx', 0.5):.3f}, "
+              f"{getattr(fp, '_cy', 0.5):.3f})  r={getattr(fp, '_radius', 0.2):.3f}")
+
+    # ── 7. Compute fine-FEM reference ONCE on initial mesh ──
+    n_init = env.mesh.t.shape[1]
+    print(f"[Test] Initial mesh: {n_init} elements")
+    print(f"[Test] Computing fine-FEM reference (n_refine_vertex={n_refine_vertex}, "
+          f"n_refine_grid={n_refine_grid}, grid={grid_resolution})...")
+
+    t0 = time.time()
+    u_ref_initial, ref_mesh, ref_sol = _compute_fine_fem_reference(env, n_refine=n_refine_vertex)
+    ref_grid = _compute_ref_grid(env, n_refine=n_refine_grid, resolution=grid_resolution)
+    print(f"[Test] Reference ready ({time.time() - t0:.1f}s, grid {ref_grid['X'].shape})")
+
+    # ── 8. Run inference ──
+    stem = output_path.rsplit(".", 1)[0] if "." in output_path else output_path
+    init_mesh = env.mesh
+    init_sol = env.scalar_solution
+    init_err = _compute_step_error(init_sol, u_ref_initial)
+    steps = [(init_mesh, init_sol, init_err, env.num_agents, u_ref_initial)]
+
+    n_elem_init = env.num_agents
+    print(f"  Step  0: reward=---  err={init_err:.4f}  elements={n_elem_init}")
+
+    done = False
+    step_idx = 0
+    total_reward = 0.0
+    while not done:
+        obs_g = obs.to(dev)
+        with torch.no_grad():
+            actions, _, _ = model(Batch.from_data_list([obs_g]), deterministic=True)
+        obs, reward, done, info = env.step(actions.cpu().numpy())
+        step_r = float(np.sum(reward))
+        total_reward += step_r
+        step_idx += 1
+
+        # Interpolate cached reference to current mesh vertices (no re-solve)
+        u_ref_current = _interpolate_ref_to_mesh(env.mesh.p.T, ref_mesh, ref_sol)
+        step_err = _compute_step_error(env.scalar_solution, u_ref_current)
+        steps.append((env.mesh, env.scalar_solution, step_err, env.num_agents,
+                      u_ref_current))
+
+        print(f"  Step {step_idx:2d}: reward={step_r:+.4f} err={step_err:.4f}  "
+              f"elements={info.get('num_elements', '?')}  "
+              f"sel={info.get('selected_count', 0)}  "
+              f"done={done}")
+
+    print(f"\n[Test] total_reward={total_reward:.4f}  final_err={steps[-1][2]:.4f}  "
+          f"final_elements={steps[-1][3]}")
+
+    # ── 9. Visualize ──
+    _save_pngs(steps, stem, checkpoint_path, k_test, geometry, env, ref_grid)
+    print(f"[Viz] Done → {output_path}")
+
+
+# ═══════════════════════════════════════════════════════════════════════
+#  CLI
+# ═══════════════════════════════════════════════════════════════════════
+
+def _load_yaml(path: str) -> dict:
+    """Load a YAML file, resolving relative paths against project root."""
+    import yaml
+    if not os.path.isabs(path):
+        path = os.path.join(_project_root, path)
+    with open(path, "r") as f:
+        return yaml.safe_load(f)
+
+
+def main():
+    parser = argparse.ArgumentParser(
+        description="Test AFEM trained model on alternative scatterer geometries")
+
+    # Config
+    parser.add_argument("--config", default="src/test_config.yaml",
+                        help="Test config YAML (default: src/test_config.yaml)")
+
+    # Test scenario overrides
+    parser.add_argument("--geometry", choices=["square", "multi_circle", "circle"],
+                        help="Scatterer geometry (overrides config)")
+    parser.add_argument("--checkpoint", help="Model checkpoint path (overrides config)")
+    parser.add_argument("--output", help="Output image path (overrides config)")
+    parser.add_argument("--seed", type=int, help="Random seed (overrides config)")
+    parser.add_argument("--k-test", type=float, help="Wave number (overrides config)")
+
+    # Scatterer overrides
+    parser.add_argument("--cx", type=float, help="Scatterer center x")
+    parser.add_argument("--cy", type=float, help="Scatterer center y")
+    parser.add_argument("--radius", type=float, help="Scatterer radius (circle)")
+    parser.add_argument("--eps-r", type=float, help="Dielectric constant eps_r")
+    parser.add_argument("--half-side", type=float, help="Half side length (square)")
+    parser.add_argument("--angle", type=float, help="Rotation angle in radians (square)")
+    parser.add_argument("--circles", nargs="*", default=None,
+                        help="Circle specs: 'cx,cy,radius[,eps_r]' (multi_circle)")
+
+    # Reference computation overrides
+    parser.add_argument("--n-refine-vertex", type=int,
+                        help="Uniform refinement levels for vertex error reference")
+    parser.add_argument("--n-refine-grid", type=int,
+                        help="Uniform refinement levels for grid heatmap reference")
+    parser.add_argument("--grid-resolution", type=int,
+                        help="Grid resolution N for heatmap (N x N)")
+
+    args = parser.parse_args()
+
+    # ── Load test config ──
+    test_cfg = _load_yaml(args.config)
+
+    # ── Load base config ──
+    base_config_path = test_cfg.get("base_config", "src/config.yaml")
+    base_config = _load_yaml(base_config_path)
+
+    # ── Build CLI overrides dict (only non-None values) ──
+    cli_overrides = {}
+    for key in ("geometry", "checkpoint", "output", "seed", "k_test",
+                "cx", "cy", "radius", "eps_r", "half_side", "angle",
+                "n_refine_vertex", "n_refine_grid", "grid_resolution"):
+        val = getattr(args, key.replace("-", "_"), None)
+        if val is not None:
+            cli_overrides[key] = val
+
+    # Parse --circles if provided
+    if args.circles is not None:
+        circles = []
+        for spec in args.circles:
+            parts = [float(x.strip()) for x in spec.split(",")]
+            circles.append({
+                "cx": parts[0], "cy": parts[1], "radius": parts[2],
+                "eps_r": parts[3] if len(parts) > 3 else 3.0,
+            })
+        cli_overrides["circles"] = circles
+
+    # ── Set seeds ──
+    seed = cli_overrides.get("seed", test_cfg.get("test", {}).get("seed", 99))
+    torch.manual_seed(seed)
+    np.random.seed(seed)
+
+    test_alt_media(
+        base_config=base_config,
+        test_cfg=test_cfg,
+        cli_overrides=cli_overrides,
+    )
+
+
+if __name__ == "__main__":
+    main()
diff --git a/src/visualize.py b/src/visualize.py
index 06b2068..c9451a0 100644
--- a/src/visualize.py
+++ b/src/visualize.py
@@ -176,14 +176,13 @@ def _save_png(steps, stem, checkpoint_path, k, cx=0.5, cy=0.5, radius=0.2, eps_r
             if im2 is not None:
                 fig2.colorbar(im2, ax=axes2[1], fraction=0.046, pad=0.04)
 
-            # ── Panel 3: ||FEM| - |Mie|| error ──
-            mie_abs = np.abs(u_mie_at_verts)
-            error_abs = np.abs(coarse_val - mie_abs)
+            # ── Panel 3: |FEM − Mie| complex error ──
+            error_abs = np.abs(scalar - u_mie_at_verts)  # complex difference, preserves phase
             evmin, evmax = 0.0, error_abs.max() or 1.0
             if evmax - evmin < 1e-12:
                 evmax = evmin + 1.0
             tcf3 = _render_field(axes2[2], pts[:, 0], pts[:, 1], tg_coarse, error_abs,
-                                 f"||FEM|-|Mie||  L2={err_val:.4f}  max={error_abs.max():.4f}",
+                                 f"|FEM − Mie|  L2={err_val:.4f}  max={error_abs.max():.4f}",
                                  evmin, evmax, show_mesh=True, cmap="hot")
             axes2[2].add_patch(plt.Circle((cx, cy), radius, fill=False,
                                           edgecolor="cyan", linewidth=1.5, linestyle="--"))
@@ -240,6 +239,10 @@ def visualize(config: dict, checkpoint_path: str, output_path: str = "result/vis
     init_mesh = env.mesh
     init_sol = env.scalar_solution
     init_err = _compute_step_error(env, u_mie_ref)
+    init_aw = _compute_area_weighted_error(env, u_mie_ref)
+    print(f"  Step  0: verts={init_mesh.p.shape[1]} elem={env.num_agents} "
+          f"mie_err={init_err:.4f}  aw_rel={init_aw['rel_err']*100:.2f}%  "
+          f"aw_rmse={init_aw['w_rmse']:.4f}  max_err={init_aw['max_err']:.4f}")
     steps = [(init_mesh, init_sol, init_err, env.num_agents, u_mie_ref)]
 
     print(f"[Viz] Running inference...")
@@ -259,10 +262,24 @@ def visualize(config: dict, checkpoint_path: str, output_path: str = "result/vis
         diag_n_elig = int(getattr(env, "_diag_eligible_ratio", 0) * env.num_agents)
         diag_n_mask = int(getattr(env, "_diag_masked_ratio", 0) * env.num_agents)
         remaining = getattr(env, "_n_budget", 0) - env.num_agents
+        step_aw = _compute_area_weighted_error(env, u_mie_current)
+        # timing
+        _timing = env.fem_problem.last_solve_timing
+        _t_str = ""
+        if _timing is not None:
+            _t_str = (f"  [timing] K={_timing['assemble_K']*1e3:.1f}ms"
+                      f"  f={_timing['assemble_f']*1e3:.1f}ms"
+                      f"  bnd={_timing['assemble_boundary']*1e3:.1f}ms"
+                      f"  solve={_timing['solve']*1e3:.1f}ms"
+                      f"  total={_timing['total']*1e3:.1f}ms"
+                      f"  n_dof={_timing['n_dof']}")
+
         print(f"  Step {step_idx}: verts={env.mesh.p.shape[1]} elem={n_elem} "
-              f"mie_err={step_err:.4f} "
+              f"mie_err={step_err:.4f}  aw_rel={step_aw['rel_err']*100:.2f}%  "
+              f"aw_rmse={step_aw['w_rmse']:.4f}  max_err={step_aw['max_err']:.4f}  "
               f"sel={diag_n_sel} elig={diag_n_elig} masked={diag_n_mask} "
-              f"remaining={remaining} done={done}")
+              f"remaining={remaining} done={done}"
+              f"{_t_str}")
 
         steps.append((env.mesh, sol, step_err, n_elem, u_mie_current))
 
@@ -283,6 +300,41 @@ def _compute_step_error(env, u_mie_ref) -> float:
     return float(np.linalg.norm(diff) / denom)
 
 
+def _compute_area_weighted_error(env, u_mie_ref):
+    """Area-weighted relative error FEM vs Mie (triangle-level quadrature)."""
+    if u_mie_ref is None:
+        return {"rel_err": float("nan"), "w_rmse": float("nan"), "max_err": float("nan")}
+    mesh = env.mesh
+    pts = mesh.p.T
+    tri = mesh.t.T
+    u_fem = env.scalar_solution
+
+    err_abs = np.abs(u_fem - u_mie_ref)
+    ref_abs = np.abs(u_mie_ref)
+
+    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])
+    )
+
+    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
+
+    total_area = np.sum(tri_areas)
+    w_rmse = np.sqrt(np.sum(err_tri_sq * tri_areas) / total_area)
+
+    ref_total = np.sum(ref_tri_sq * tri_areas)
+    rel_err = np.sqrt(np.sum(err_tri_sq * tri_areas) / ref_total) if ref_total > 1e-12 else float("nan")
+
+    return {"rel_err": float(rel_err), "w_rmse": float(w_rmse),
+            "max_err": float(np.max(err_abs))}
+
+
 def _eval_mie_on_mesh(env, mie_info):
     """Re-evaluate Mie scattered field on current FEM mesh vertices."""
     if mie_info is None:
diff --git a/sync.ps1 b/sync.ps1
index 0d0f9be..42469c3 100644
--- a/sync.ps1
+++ b/sync.ps1
@@ -2,7 +2,7 @@
 $ServerA_User = "dxw"
 $ServerA_IP = "222.20.97.222"
 $RemotePath = "/public/home/dxw/Codes/afem"  # 服务器A上项目的绝对路径
-$LocalPath = "F:\ASMRplusplus-main"             # 本地项目路径
+$LocalPath = "F:\mine\afem"             # 本地项目路径
 # ==========================================
 
 Write-Host ">>> Step 1: Downloading code from Server A..." -ForegroundColor Cyan
diff --git a/train.sh b/train.sh
new file mode 100644
index 0000000..34b63d6
--- /dev/null
+++ b/train.sh
@@ -0,0 +1,22 @@
+#!/bin/bash
+
+#SBATCH --job-name=afem-train
+#SBATCH --partition=gpu
+#SBATCH --gres=gpu:1
+#SBATCH --nodelist=node06
+#SBATCH --cpus-per-task=4
+#SBATCH --mem=32G
+#SBATCH --time=24:00:00
+#SBATCH --output=logs/train_%j.out
+
+# cd /public/home/dxw/Codes/afem
+
+
+
+echo "Starting training at $(date)"
+
+echo "Running on node: $(hostname)"
+
+python -u src/main.py --mode train --config src/config.yaml
+
+echo "Training finished at $(date)"
diff --git a/流程.txt b/流程.txt
deleted file mode 100644
index e69de29..0000000