Physics-Informed Graph Neural Networks for Water Distribution Systems

TL;DR

This paper tackles hydraulic state estimation in water distribution systems by introducing a physics-informed emulator that combines a local GCN (f1) with a global, non-learned hydraulics solver (f2). The two-component architecture operates in an unsupervised learning loop, inferring heads and flows from reservoir heads and demands while enforcing mass-balance and head-loss physics via an iterative fixed-point scheme. The method achieves substantial speedups over the traditional EPANET simulator on five real-world WDS, while maintaining high accuracy in head and demand reconstruction and reasonable flow estimates, even under perturbations to demands and diameters. This work enables rapid, scalable planning and expansion of critical water Infrastructure through physics-guided neural surrogates, with potential extensions to valves, pumps, and PDD scenarios.

Abstract

Water distribution systems (WDS) are an integral part of critical infrastructure which is pivotal to urban development. As 70% of the world's population will likely live in urban environments in 2050, efficient simulation and planning tools for WDS play a crucial role in reaching UN's sustainable developmental goal (SDG) 6 - "Clean water and sanitation for all". In this realm, we propose a novel and efficient machine learning emulator, more precisely, a physics-informed deep learning (DL) model, for hydraulic state estimation in WDS. Using a recursive approach, our model only needs a few graph convolutional neural network (GCN) layers and employs an innovative algorithm based on message passing. Unlike conventional machine learning tasks, the model uses hydraulic principles to infer two additional hydraulic state features in the process of reconstructing the available ground truth feature in an unsupervised manner. To the best of our knowledge, this is the first DL approach to emulate the popular hydraulic simulator EPANET, utilizing no additional information. Like most DL models and unlike the hydraulic simulator, our model demonstrates vastly faster emulation times that do not increase drastically with the size of the WDS. Moreover, we achieve high accuracy on the ground truth and very similar results compared to the hydraulic simulator as demonstrated through experiments on five real-world WDS datasets.

Figures (12)

• Figure 1: The model architecture: The local GCN model $f_1$ learns from the global physics-informed algorithm $f_2$ through multiple iterations.
• Figure 2: The flow $q_{e_{uv}}$ from node $u$ to $v$ has to be equal to the negative of the flow $q_{e_{vu}}$ from $v$ to $u$.
• Figure 3: The sum of inflows $q_{1,0}, q_{3,0}$ and outflow $q_{0,2}$ must be equal to the negative of the demand $d_{0}$ at node $0$.
• Figure 4: The relationship between pressure heads at neighbouring nodes and the flow in connecting pipe.
• Figure 5: Comparison of simulation/emulation times on L-TOWN Area-C for EPANET and GCN Model.

Theorems & Definitions (41)

• Lemma 3.1
• proof
• Theorem 3.2
• proof
• Theorem 3.3
• proof
• Lemma A.1
• proof
• Definition A.2: Paths
• Theorem A.4