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

Area of Science:

• Hydraulic Engineering
• Data Science
• Network Science

Background:

• Accurate hydraulic state estimation is crucial for Water Distribution Network (WDN) observability and decision-making.
• Existing data-driven models struggle to jointly infer network-wide states and their future dynamics.
• Physics-based solvers are computationally expensive, necessitating efficient alternatives.

Purpose of the Study:

• To propose a Physics-Informed Graph Inference and Prediction (PhiGIP) framework for global hydraulic state estimation in WDNs.
• To enable accurate inference and multi-step forecasting of nodal and pipe states using sparse pressure observations.
• To develop a cost-effective and robust surrogate modeling approach for data-limited WDNs.

Main Methods:

• Integrated a graph neural network (GNN) to model dynamic pressure evolution.
• Formulated global head estimation as a graph spectral low-frequency inference problem.
• Employed a globally coupled optimization for pipe flow estimation, ensuring physical consistency without simulation labels.

Main Results:

• On benchmark networks with 5% pressure coverage, nodal head errors were below 0.2m (LTown) and 2m (KL), with pipe flow errors under 5%.
• In a real-world WDN, PhiGIP inferred states for over 16,000 nodes and pipes using only 12 pressure measurements.
• Achieved Mean Absolute Error (MAE) below 2m for pressure nodes and Mean Absolute Percentage Error (MAPE) around 10% for monitored pipe flows.

Conclusions:

• PhiGIP offers an accurate, robust, and lightweight surrogate modeling approach for hydraulic inference and forecasting in WDNs.
• Demonstrates practical potential for operational scheduling, anomaly detection, and intelligent water system management.
• Addresses the challenge of data scarcity in WDN monitoring and analysis.