Interval Estimation in Water Distribution Systems Using Physics-Informed Graph Neural Networks

Abstract

Abstract Artificial Intelligence in general and Machine Learning (ML) in particular has the potential to play a key role in critical infrastructure such as Water Distribution Systems (WDSs). In the face of urban population growth, ML can pave the way towards smart cities by not only solving various tasks in WDSs but also dealing with emerging uncertainties in WDSs. For instance, demands can be subject to uncertainty intervals and pipe attributes may vary over time. This study presents a novel physics-informed Graph Neural Network (GNN) based model for WDSs that predicts output feature intervals, given the input feature intervals. A comprehensive training scheme is developed to map multiple input intervals to the corresponding multiple output intervals. To address the varying ranges and magnitudes of state variables in WDSs, we introduce a theoretically grounded, reversible, and physics-preserving data normalization method. The proposed model demonstrates strong performance across five WDS datasets, achieving results comparable to those of the computationally intensive Monte Carlo sampling method.