Graph-Structured Physics-Informed Deep Operator Network for Simulating Hydrodynamics of Tidal River Networks

Abstract

This study proposes a surrogate model, Graph-Structured Physics-Informed Deep Operator Network (GS-PI-DeepONet), to simulate two-dimensional hydrodynamics in a tidal river network. The model was coupled with Graph Convolutional Networks (GCNs) for spatial feature extraction and Long Short-Term Memory (LSTM) network for temporal prediction, with 2D shallow-water equations (2D SWEs) embedded as physical constraints. To handle complex river network topologies, a mapping mechanism was proposed to transform discrete irregular boundaries into differentiable neural network constraints. A dynamic weighting strategy was developed to improve model training efficiency. GS-PI-DeepONet was applied to a river network within the Pearl River Basin in Zhuhai. Trained on high-fidelity Delft3D data, it achieved precise flow field reconstruction and millisecond-level extrapolation predictions, outperforming traditional data-driven models. The model can be a valuable tool for real-time hydrodynamic simulations and flood management strategies in tidal river networks.