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

arXiv: https://arxiv.org/abs/2607.25148 · HTML: https://mlsanity.com/paper/2607.25148/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 29 references that are in the map.
- First posted on arXiv 27 Jul 2026.

## Builds on (most cited first, 15 of 15)

- [Encoder-Decoder with Atrous Separable Convolution for Semantic Image Segmentation](https://mlsanity.com/paper/1802.02611/) (2018)
- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [Generalised Dice overlap as a deep learning loss function for highly unbalanced segmentations](https://mlsanity.com/paper/1707.03237/) (2017)
- [Theory-guided Data Science: A New Paradigm for Scientific Discovery from Data](https://mlsanity.com/paper/1612.08544/) (2016)
- [Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systems](https://mlsanity.com/paper/2003.04919/) (2020)
- [Emotions Don't Lie: An Audio-Visual Deepfake Detection Method Using Affective Cues](https://mlsanity.com/paper/2003.06711/) (2020)
- [TraPHic: Trajectory Prediction in Dense and Heterogeneous Traffic Using Weighted Interactions](https://mlsanity.com/paper/1812.04767/) (2018)
- [M3ER: Multiplicative Multimodal Emotion Recognition Using Facial, Textual, and Speech Cues](https://mlsanity.com/paper/1911.05659/) (2019)
- [EmotiCon: Context-Aware Multimodal Emotion Recognition using Frege's Principle](https://mlsanity.com/paper/2003.06692/) (2020)
- [Flood Prediction Using Machine Learning Models: Literature Review](https://mlsanity.com/paper/1908.02781/) (2019)
- [STEP: Spatial Temporal Graph Convolutional Networks for Emotion Perception from Gaits](https://mlsanity.com/paper/1910.12906/) (2019)
- [Forecasting Trajectory and Behavior of Road-Agents Using Spectral Clustering in Graph-LSTMs](https://mlsanity.com/paper/1912.01118/) (2019)
- [MC-LSTM: Mass-Conserving LSTM](https://mlsanity.com/paper/2101.05186/) (2021)
- [RobustTP: End-to-End Trajectory Prediction for Heterogeneous Road-Agents in Dense Traffic with Noisy Sensor Inputs](https://mlsanity.com/paper/1907.08752/) (2019)
- [Data-driven Flood Emulation: Speeding up Urban Flood Predictions by Deep Convolutional Neural Networks](https://mlsanity.com/paper/2004.08340/) (2020)

## Abstract (arXiv)

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.