Graph Neural Networks for State Estimation in Water Distribution Systems: Application of Supervised and Semisupervised Learning

Emerging trends of resilient and reliable water infrastructure advocate for the development of efficient state estimation (SE) techniques in water distribution systems (WDSs). SE refers to estimating the flows and heads in the WDS at unmonitored locations based on measurements collected from limited monitoring locations. Current physics-based SE methods typically require more exhaustive than readily available information about the WDS and are computationally demanding to attain real-time SE fully. Using neural networks for SE is a promising avenue because neural networks are more adaptable to the availability of sensory data and can shift most of the computation efforts to the offline training phase. Once trained, the inference is more computationally efficient compared to the physics-based SE methods. This work proposes a graph neural network (GNN) model for SE in WDSs. Unlike traditional neural networks, GNNs are more suitable for the SE problem for two main reasons: (1) given a limited number of monitoring locations, the SE problem inherently requires a semisupervised learning method, and (2) GNNs enable learning from the graph structure of a WDS, thus providing a mechanism to incorporate the functional relationships between the monitored and unmonitored locations and incorporate the physical laws during the training process. To evaluate the performance of GNNs for SE, we tested supervised and semisupervised approaches, investigated the impact of GNN architecture choices on its performance, and examined model performance under different levels of noise in the training data. The results demonstrate that GNNs are promising for SE for their ability to learn from graph structure with a limited amount of information while exhibiting robustness to noise. This study contributes toward advancing real-time GNN-based SE in WDSs. Future research is needed to incorporate various hydraulic devices and investigate the scalability of GNNs to large-scale WDSs.