Physics-Informed CNN-LSTM for Street-Scale Urban Flood Prediction: Reconciling Aggregate Accuracy and Street-Level Plausibility

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.