Physics-Informed Deep Learning model for Hurricane-Induced Compound Flooding

Physics-based hydrodynamic models are widely used to simulate compound flooding processes because they explicitly represent the governing physical mechanisms. However, these models are computationally expensive, particularly when high spatial resolution and large ensembles of storm scenarios are required. Such computational demands limit their applicability for rapid analysis, uncertainty quantification, and real-time forecasting. On the other hand, purely data-driven (DD) surrogate models based on deep learning can significantly accelerate prediction once trained, but they often lack physical consistency and may produce unrealistic results when extrapolating beyond the conditions represented in the training data.

To address this limitation, we incorporate physics constraints derived from the finite-difference formulation of the governing partial differential equations (PDEs) directly into the deep learning loss function. By embedding these constraints during training, the model is encouraged to produce predictions that are not only accurate but also consistent with the underlying physical processes governing flood dynamics. This physics-informed machine learning (PIML) framework effectively combines the computational efficiency of data-driven models with the physical reliability of process-based models.

To evaluate the effectiveness of this approach, we conduct systematic benchmarking using seven hurricane scenarios with varying characteristics. These experiments are designed to assess where, when, and under what conditions the physics constraints provide the greatest benefit for compound flooding prediction. The results show that the PIML model consistently outperforms the purely data-driven model under both in-distribution and out-of-distribution conditions. In particular, the incorporation of physics constraints improves prediction stability in inland areas and hydrodynamically active regions during peak flooding. By constraining abrupt and physically inconsistent water-level responses, the PIML framework produces more reliable and physically realistic flood predictions, highlighting its potential for improving surrogate modeling of compound flood hazards.