Graph Neural Networks for Pressure Estimation in Water Distribution Systems

TL;DR

This work tackles pressure estimation in water distribution networks under partial observability and distribution shifts by combining physics-based data generation with a graph neural network, GATRes. The method uses random sensor placement, time-relevant evaluation with realistic demand patterns and noise, and a multi-graph pre-training strategy to enable generalization to unseen WDNs. It achieves state-of-the-art accuracy, with $\text{MAE} = 1.94\ \mathrm{mH_2O}$ and $\text{MAPE} = 7\%$ on a large Dutch network, and up to $\approx 52\%$ improvement on benchmark networks, while maintaining robust performance under varying sensor configurations. The approach supports practical deployment in digital twins and real-time monitoring by balancing physics-informed data generation with scalable GNN inference, and it points to future work in physics-regularized learning and broader cross-network generalization.

Abstract

Pressure and flow estimation in Water Distribution Networks (WDN) allows water management companies to optimize their control operations. For many years, mathematical simulation tools have been the most common approach to reconstructing an estimate of the WDN hydraulics. However, pure physics-based simulations involve several challenges, e.g. partially observable data, high uncertainty, and extensive manual configuration. Thus, data-driven approaches have gained traction to overcome such limitations. In this work, we combine physics-based modeling and Graph Neural Networks (GNN), a data-driven approach, to address the pressure estimation problem. First, we propose a new data generation method using a mathematical simulation but not considering temporal patterns and including some control parameters that remain untouched in previous works; this contributes to a more diverse training data. Second, our training strategy relies on random sensor placement making our GNN-based estimation model robust to unexpected sensor location changes. Third, a realistic evaluation protocol considers real temporal patterns and additionally injects the uncertainties intrinsic to real-world scenarios. Finally, a multi-graph pre-training strategy allows the model to be reused for pressure estimation in unseen target WDNs. Our GNN-based model estimates the pressure of a large-scale WDN in The Netherlands with a MAE of 1.94mH$_2$O and a MAPE of 7%, surpassing the performance of previous studies. Likewise, it outperformed previous approaches on other WDN benchmarks, showing a reduction of absolute error up to approximately 52% in the best cases.

Figures (9)

• Figure 1: Density Distribution of training and test sets in C-Town, Richmond, L-Town and Oosterbeek WDNs, generated by the Hydraulic Simulation tool EPANET.
• Figure 2: Our data generation approach. Dynamic parameters are sampled from a uniform distribution and passed to the mathematical simulation with static values and WDN topology. The result is a synthetic dataset containing legit snapshots whose pressure range should be close to reality.
• Figure 3: GATRes architecture. The left image indicates the overall architecture consists of two linear layers interleaving with GATRes blocks. The middle figure illustrates the abstract view in each block. The right-side ones explain the message aggregation mechanism between neighbor nodes.
• Figure 4: Graph Neural Network training scheme. Given clean snapshots, we mask out a significant number (95%) of node features. The remaining data is then sent into a GNN playing as an autoencoder to rebuild missing values with regard to graph properties (such as topology and edge attributes). GNN weights are updated using the loss derived by the predicted and ground truth values at masked places.
• Figure 5: Water Distribution Networks used in this study.