Physics-Informed Graph Neural Networks for Leak Diagnosis Under Concurrent Leakage

Leakage diagnosis in water distribution networks is constrained by sparse instrumentation, uncertain models, and leak concurrency. We present a physics-informed spatio-temporal graph neural network evaluated end-to-end on the open Battle of the Leakage Detection and Isolation Methods (BattLeDIM) and L-Town benchmark (782 junctions, 905 pipes, 33 pressure sensors). Message passing operates on a conductance-weighted hydraulic Laplacian, trained by self-supervised sensor masking to reconstruct nodal pressure fields and latent pipe flows, embedding Hazen-Williams energy and mass-balance residuals in the loss under learned uncertainty weighting. Pressure at withheld sensors is reconstructed to 0.29 meters. A seeded ablation shows physical constraints degrade reconstruction accuracy by 0.10 meters of head while reducing nodal continuity violations by over five orders of magnitude, rendering the inferred state hydraulically admissible. Residuals feed two complementary detectors. A level-based statistic saturates under concurrent leakage; pairing it with a two-window onset contrast raises detection from 13 to 22 of 23 ground-truth leaks (95.7 %, 95 % confidence interval 79.0–99.2 %), with median detection times of 29 hours for abrupt and 74 hours for incipient events, releasing 96 % of annual leaked volume after detection. Localization transfers poorly from simulation, with a median error of 857 meters and only three leaks meeting the joint 300 meters criterion due to signal superposition under concurrency.