Explicit Water Balance Constraints for Trustworthy Graph Neural Network Flood Forecasting

Although Graph Neural Networks (GNNs) are widely regarded as an ideal tool for capturing spatial dependencies in river basins, their effectiveness in hydrological forecasting is severely challenged by a topology paradox: under a purely data-driven paradigm, GNNs fail to spontaneously learn physical laws, generating predictions that lack physical interpretability and frequently violate mass conservation. To address this fundamental problem, this paper proposes a physics-informed graph learning framework integrated with an explicit, differentiable water balance constraint (WB-GNN). By reconstructing the continuity equation into a differentiable loss function, we directly embed physical conservation as a strong inductive bias into the neural network’s training objective. We comprehensively evaluated the model on two large-sample datasets (LamaH-CE and CAMELS) against state-of-the-art baselines, including EA-LSTM and unconstrained Pure-GNN. Quantitative results demonstrate that the proposed physical constraint successfully awakens the potential of river network topology. On the LamaH-CE dataset, WB-GNN achieved a Nash-Sutcliffe Efficiency (NSE) of 0.86 and a Root Mean Square Error (RMSE) of 9.2 m3/s, outperforming both the domain-specific EA-LSTM (NSE: 0.83) and the unconstrained Pure-GNN (NSE: 0.74). Crucially, the introduction of the differentiable constraint reduced the Physical Inconsistency Ratio (PIR) by an order of magnitude-from 39.8% in the unconstrained model to just 4.3%. Similar robust improvements were validated across the highly heterogeneous CAMELS dataset. These quantifiable results confirm that the proposed method not only achieves superior forecasting accuracy but also fundamentally guarantees physical trustworthiness, making it highly robust for critical decision-making in extreme flood events.