A Physical-Enhanced Spatio-Temporal Graph Convolutional Network for River Flow Prediction

River flow forecasting remains a critical yet challenging task in hydrological science, owing to the inherent trade-offs between physics-based models and data-driven methods. While physics-based models offer interpretability and process-based insights, they often struggle with real-world complexity and adaptability. Conversely, purely data-driven models, though powerful in capturing data patterns, lack physical grounding and often underperform in extreme scenarios. To address this gap, we propose PESTGCN, a Physical-Enhanced Spatio-Temporal Graph Convolutional Network that integrates hydrological domain knowledge with the flexibility of graph-based learning. PESTGCN models the watershed system as a Heterogeneous Information Network (HIN), capturing various physical entities (e.g., gauge stations, rainfall stations, reservoirs) and their diverse interactions (e.g., spatial proximity, rainfall influence, and regulation effects) within a unified graph structure. To better capture the latent semantics, meta-path-based encoding is employed to model higher-order relationships. Furthermore, a hybrid attention mechanism incorporating both local temporal features and global spatial dependencies enables comprehensive sequence learning. Importantly, key variables from the HEC-HMS hydrological model are embedded into the framework to improve physical interpretability and generalization. Experimental results on four real-world benchmark watersheds demonstrate that PESTGCN achieves statistically significant improvements over existing state-of-the-art models, with relative reductions in MAE ranging from 5.3% to 13.6% across different forecast horizons. These results validate the effectiveness of combining physical priors with graph-based temporal modeling.