Physics-Informed Spatiotemporal Graph Convolutional Network for Flash Flood Forecasting and Inundation Simulation

Abstract. Flash floods pose a significant threat in mountainous regions, where rapid-onset inundation requires timely and reliable forecasting for effective emergency response. Physically based hydrodynamic models provide strong interpretability but require detailed terrain, roughness, rainfall, and initial-condition information, and their computational cost limits real-time forecasting and repeated scenario analysis. Data-driven models offer higher efficiency, but grid-based architectures may distort irregular hydrodynamic meshes, and purely data-driven graph models can generate physically implausible predictions during long-horizon autoregressive simulation. To address these limitations, this study proposes a physics-informed spatiotemporal graph convolutional network, termed PI-STGCN, for rapid flash flood inundation simulation over irregular triangular control-volume meshes. The model represents the hydrodynamic domain as a directed dual graph, where triangular cells are treated as nodes and shared interfaces are treated as directed edges with geometric and hydraulic attributes. PI-STGCN integrates edge-conditioned spatial graph convolution, rainfall encoding, causal temporal convolution, multi-step residual prediction, and rollout-aware training through scheduled sampling and pushforward rollout. Shallow-water-equation residuals, water-volume consistency, and near-channel boundary constraints are used as soft physical regularization terms to improve local hydrodynamic plausibility. The model was trained using hydrodynamic simulation outputs from design storm events and evaluated on an unseen 100a24h extreme design storm and an independent real rainfall-driven flash flood event. For the 100a24h event, PI-STGCN achieved R² = 0.9142, NSE = 0.9088, KGE = 0.8565, MAE = 0.3390, and RMSE = 0.7892. Ablation and residual diagnostics show that spatial graph convolution and residual prediction are critical for accuracy and rollout stability, while physics-informed regularization improves momentum-equation consistency, although its effect on conventional predictive metrics is event- and metric-dependent. The trained model reduced inference time from 63–105 s for hydrodynamic simulations to 1.06–1.08 s. These results indicate that PI-STGCN provides an efficient physics-regularized surrogate for rapid inundation prediction on irregular meshes in mountainous catchments.