Physics-informed hydrological graph neural network for distributed daily streamflow prediction in directed river networks

The basin in high-altitude mountainous areas is constrained by sparse station networks, complex river networks, and significant non-stationary hydrological processes, making it difficult for traditional time series models to simultaneously consider spatial connectivity and physical consistency. To address this issue, we propose Physics-Informed Hydrological Graph Neural Network (PI-HydroGNN) for distributed daily streamflow prediction in directed river networks. It combines temporal feature extraction, upstream connectivity and topological inflow aggregation, graph-based topology message passing, and physical constraints in a unified framework to represent temporal dynamics, river-network connectivity, and local mass conservation. The model was evaluated through comparisons with independent station-wise LSTM, regional multi-output LSTM, GCN and SWAT, together with ablation experiments, multi-step forecasting, analysis of Quality Balance Violations and ungauged basin extrapolation. The results showed that PI-HydroGNN outperformed the benchmark models in the training, validation, and testing periods, with an average NSE of 0.84 during the testing period and a RMSE reduction of about 16% compared to station-wise LSTM. The ablation experiment results showed that all the modules we considered made significant contributions to the predictive performance and exhibited significant spatial heterogeneity. At Yangbajing, the model still maintains good simulation ability, with an NSE of 0.79 and an R 2 of 0.80, providing preliminary evidence of its spatial extrapolation capability. Overall, this study demonstrates that combining prior knowledge of hydrological physics with graph learning offers a promising approach for streamflow prediction in complex river networks, and suggests potential for application in ungauged basins that should be further validated under broader hydro-climatic conditions.