用物理约束提升城市洪水预测的街道级合理性，避免水往高处流。
Physics-Informed CNN-LSTM for Street-Scale Urban Flood Prediction: Reconciling Aggregate Accuracy and Street-Level Plausibility
- 在损失函数中加入重力、质量守恒和地形感知三项物理惩罚项。
- 街道级召回率提升至0.77，远超基线模型的0.44，且几乎无反重力错误。
- 适合交通导航等需精准街道洪水信息的应用场景。
基于均方误差训练的深度学习模型虽统计准确，却可能产生水往高处流、凭空出现或街巷水流平滑等不合理的洪水预测。本文构建了针对CNN-LSTM模型的物理信息训练框架，以15分钟间隔预测128×128网格上的城市洪涝深度。在损失函数中引入三项可微分惩罚项：(i) 重力损失，惩罚逆水位梯度的深度增加；(ii) 连续性损失，结合降雨自适应阈值保证局部质量守恒；(iii) 地形感知误报惩罚，由地形湿润指数（TWI）调节。在弗吉尼亚诺福克市两场风暴事件（2017年8月与2022年9月，共300样本）数据集上评估，所有模型使用相同划分，通过重复随机划分与留一风暴测试验证鲁棒性。限定于由TWI导出的街道掩膜区域进行道路邻近评估，物理约束模型实现近零重力违规（约1e-6），街道通道召回率达0.77±0.09（基线为0.44±0.10），对交通路径规划最为关键；其优势在独立风暴测试中翻倍。统一误报惩罚变体虽使平均绝对误差降低16%，但街道召回率降至0.25。而基于TWI调制的惩罚项在所有指标上优于均匀变体，以最低MAE实现60%更高的街道召回率，并取得最佳街道级F1分数。结果揭示了像素级误差与应用导向物理合理性之间的根本矛盾，证明地形感知损失调制是一种原则性解决方案。
原文摘要 · Abstract (English)
Deep learning surrogate models trained with mean-squared-error loss produce statistically accurate but physically unconstrained flood predictions: water may flow uphill, appear spontaneously, or smooth over street-level corridors. We develop a physics-informed training framework for CNN-LSTM models that predict urban flood depths at 15 min intervals over a 128x128 spatial grid. Three differentiable penalty terms are embedded into the loss: (i) a gravity loss penalizing depth increases against the water-surface-elevation gradient, (ii) a continuity loss enforcing local mass conservation with rainfall-adaptive thresholds, and (iii) a topography-aware false-alarm penalty modulated by the topographic wetness index (TWI). We evaluate on the Norfolk, Virginia flood dataset spanning two storm events (August 2017 and September 2022, 300 samples), with all variants trained on identical splits and robustness assessed over repeated random splits and leave-one-storm-out tests. A road-proximal evaluation restricted to a TWI-derived street mask quantifies street-level skill. The physics-constrained model achieves near-zero gravity violations (order 1e-6) and the highest street-channel recall (0.77 +/- 0.09 vs 0.44 +/- 0.10 for the unconstrained baseline), the capability most relevant to traffic routing, and its advantage more than doubles on a held-out storm; a uniform false-alarm variant attains 16% lower mean absolute error but suppresses street recall to 0.25. The TWI-modulated penalty reconciles this trade-off: it improves on the uniform variant on every metric, recovering 60% higher street recall at the lowest MAE among constrained variants and the best street-level F1. These results expose a fundamental tension between aggregate pixel-level error and application-specific physical plausibility, and show that terrain-aware loss modulation offers a principled resolution.
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