Physics-informed neural networks for solving flow problems modeled by the 2D Shallow Water Equations without labeled data

Abstract

This paper investigates the application of physics-informed neural networks (PINNs) to solve free-surface flow problems governed by the 2D shallow water equations (SWEs). Two types of PINNs are developed and analyzed: a physics-informed fully connected neural network (PIFCN) and a physics-informed convolutional neural network (PICN). The PINNs eliminate the need for labeled data for training by employing the SWEs, initial and boundary conditions as components of the loss function to be minimized. Results from a set of idealized and real-world tests showed that the prediction accuracy and computation time (i.e., training time) of both PINNs may be less affected by the resolution of the domain discretization when compared against solutions by a Finite Volume (FV) model. Overall, the PICN shows a better trade-off between computational speed and accuracy than the PIFCN. Also, our results for the idealized problems indicated that PINNs can provide more than 5 times higher prediction accuracy than the FV model, while the FV simulation with coarse resolution (e.g., 10 m) can provide sub-centimeter accurate (RMSE) solutions at least one order of magnitude faster than the PINNs. Results from a river flood simulation showed that PINNs delivered better speed-accuracy trade-off than the FV model in terms of predicting the water depth, while FV models outperformed the PINNs for predictions of total flow discharge.