Physics-informed graph inference and prediction for global state estimation in water distribution networks

Accurate estimation of unknown hydraulic states is critical for enhancing the observability of water distribution networks (WDNs) and enabling timely and reliable decision-making. Data-driven surrogate models offer a cost-effective alternative to traditional physics-based solvers, yet few can jointly infer network-wide nodal and pipe states and their future evolution. This study proposes a Physics-Informed Graph Inference and Prediction (PhiGIP) framework for global hydraulic state estimation using sparse pressure observations. PhiGIP integrates a graph neural network to model dynamic pressure evolution and formulates global head estimation as a graph spectral low-frequency inference problem. Pipe flow estimation is then achieved through a globally coupled optimization process, ensuring physical consistency without requiring simulation-generated supervisory labels. Comprehensive evaluations were conducted on benchmark networks (LTown and KL) and a real-world WDN. On benchmark systems with 5% pressure monitoring coverage, the estimation error of most nodal heads remained below 0.2 m for LTown and 2 m for KL, while pipe flow error was generally below 5%. In the real-world case, PhiGIP inferred unknown hydraulic states of 16,567 nodes and 17,205 pipes from only 12 pressure measurements, achieving MAE below 2 m at validation pressure nodes and flow MAPE around 10% at several monitored pipes during non-peak periods. These results demonstrate that PhiGIP provides an accurate, robust, and lightweight surrogate modeling paradigm for global hydraulic inference and multi-step forecasting in data-limited WDNs, with practical potential for operational scheduling, anomaly detection, and intelligent water system management.