Physics-informed neural networks for hydrodynamic modelling in a 2D river system with complex riverbed terrains

This study explores the use of physics-informed neural networks (PINNs) to simulate river hydrodynamics over complex varying bed elevations, as surrogate models for MIKE 21, enabling the reconstruction of high-resolution river flow fields from spatially sparse data. The PINN model was incorporated with the two-dimensional shallow water equations (2D SWEs) as physical constraints, and the topographic information of the riverbed for more effective convergence. A dynamic weighting strategy was applied to improve the model training efficiency. Trained on the data generated by a validated MIKE 21 model, the PINN model could accurately reconstruct the river flow field using sparse data. As a surrogate model, the PINN model achieved an order-of-magnitude improvement in computational efficiency compared to MIKE 21. It also performed higher accuracy and stronger short-term temporal extrapolation capability compared with another data-driven Multi-Layer Perceptron (MLP) model due to the regularization imposed by physical laws. Consequently, this study presents a robust approach for rapid and accurate two-dimensional modelling of river hydrodynamics, offering critical support for flood risk early warning.