Graph neural networks for hydraulic predictions in water distribution networks: incorporating sensor data and physical constraints

• A GGNN with sensor-based initialization is proposed for hydraulic state prediction • Loose physical constraints are integrated to ensure consistent water head predictions • Binary edge weights are shown to outperform more complex weighting schemes in accuracy • The model's generalizability is validated across multiple WDNs with consistent hyperparameters • Accurate head predictions are achieved under sparse sensors, with a MAE of 0.10 m Accurately predicting hydraulic states in water distribution networks (WDNs) is essential for maintaining effective pressure management and ensuring a reliable water supply. Traditional hydraulic models, however, face significant challenges related to calibration complexities and high costs, particularly under sparse sensor conditions. This study introduces an innovative approach that integrates a gated graph neural network (GGNN) with sensor-based initialization and loose physical constraints for predicting hydraulic states in WDNs. The GGNN leverages sensor data and graph topology to improve nodal head predictions, while a physical constraint—enforcing that upstream heads are greater than downstream heads—enhances consistency. Evaluations across three distinct WDNs demonstrate the effectiveness and generalizability of the proposed method, with consistent hyperparameters applied to all networks. Across three real-world network cases, the model achieves a mean absolute error (MAE) as low as 0.10 m and a Nash–Sutcliffe Efficiency (NSE) up to 0.90. Expressed relative to typical head magnitudes, these errors correspond to ≤2% across networks, indicating practical accuracy under sparse sensing.These results underscore the robustness of sensor-based initialization and physical constraints, highlighting their contribution to accurate hydraulic state prediction even under sparse data conditions. This work provides a practical, scalable solution for hydraulic modelling of WDNs, advancing proactive urban water management. The code is available at https://github.com/Johnny328/GGNN-hydraulic-state-prediction.git .