Physical information-fused deep learning model ensembled with a subregion-specific sampling method for predicting flood dynamics

The computational prediction of flood dynamics is a long-standing problem in hydrodynamics and hydrology. Until now, conventional numerical models based on shallow water equations (SWEs) have been the dominant approaches. Here, we show that by combining a data-driven methodology with some general physical governing equations, the resulting deep learning model can enable the prediction of the long-term dynamics of dam-break floods with satisfactory accuracy. For this purpose, we propose a deep learning model using a physics-informed neural network (PINN) embedded in SWEs. Training data are reconstructed from prior-known partial numerical solutions and a novel subregion-specific sampling method that adapts well to the violent variations in flood surfaces. Various traditional cases of 2D dam-break floods are used to illustrate and validate the effectiveness of the proposed model. The results show that the proposed PINN-embedded model predicts the dam-break flood dynamics well, as observed in the numerical simulations based on SWEs, and outperforms the pure data-driven multilayer perceptron (MLP) model and a similar model with the traditional random sampling method. We also demonstrate that the PINN-embedded model improves the computational efficiency by over 3 ∼ 4 orders of magnitude compared to the traditional 2D numerical solution of SWEs. Our study showcases how numerical simulation and deep learning techniques can be coupled to investigate the details of dam-break floods.