Accelerating Steady-State Analysis in Water Distribution Systems with Physics-informed Deep Learning and Topological Signal Processing

Water distribution systems (WDS) face increasing challenges from climate change, urbanization, and growing populations, making efficient and accurate modeling crucial for their management. While traditional physics-based hydraulic models provide reliable results, they are computationally intensive, limiting their application in real-time decision-making and large-scale optimization. Our multi-year research journey demonstrates a progressive evolution in WDS modeling, successfully combining data-driven efficiency with fundamental physical principles.

Our investigations evolve from conventional neural networks to increasingly sophisticated physically-informed approaches. We demonstrate how Graph Neural Networks can leverage network topology to improve prediction accuracy, but more importantly, how reformulating the problem in the edge space allows direct embedding of mass conservation principles. This novel Edge-Based Graph Neural Network (EGNN) architecture not only achieves superior performance but also demonstrates remarkable zero-shot generalization capabilities across different network configurations.

Building on these insights, we further reformulate steady-state estimation as a diffusion process on graph edges, incorporating both mass and energy conservation laws. This physics-based reformulation enables direct GPU acceleration without relying on machine learning approximations, achieving near-perfect accuracy on multiple benchmarks while maintaining substantial computational speedups compared to traditional solvers.

We then extend this approach to handle uncertainty by developing a topological Gaussian Process framework, where the covariance structure naturally encodes the physical conservation laws. This probabilistic extension enables rapid uncertainty quantification under variable demands, providing analytical uncertainty bounds without the computational burden of Monte Carlo sampling, while preserving the physical consistency guaranteed by our diffusion-based formulation.