Interpretable physics-informed graph neural networks for flood forecasting

Climate change has intensified extreme weather events, with floods causing significant socioeconomic and environmental damage. Accurate flood forecasting is crucial for disaster preparedness and risk mitigation, yet traditional hydrodynamic models, while precise, are computationally prohibitive for real-time applications. Machine learning surrogates, such as graph neural networks (GNNs), improve efficiency but often lack physical consistency and interpretability. This paper introduces HydroGraphNet, a novel physics-informed GNN framework that, for the first time, integrates the Kolmogorov–Arnold Network (KAN) to enhance model interpretability in unstructured mesh-based flood forecasting. The framework embeds mass conservation laws into the loss function, ensuring physically consistent predictions. Additionally, it employs an autoregressive encoder–processor–decoder architecture that captures spatiotemporal flood dynamics while mitigating error accumulation over long forecasting horizons. Validation on flood data from the White River near Muncie, Indiana, demonstrates a 67% reduction in prediction error, near-zero mass balance error, and a 58% improvement in the critical success index for major flood events compared to a baseline GNN model. These results highlight the potential of the proposed framework to advance real-time flood forecasting with improved physical consistency and interpretability.