Graph Attention Networks with Physical Constraints for Anomaly Detection

Water distribution systems (WDSs) face increasing cyber-physical risks, which make reliable anomaly detection essential. Many data-driven models ignore network topology and are hard to interpret, while model-based ones depend strongly on parameter accuracy. This work proposes a hydraulic-aware graph attention network using normalized conservation law violations as features. It combines mass and energy balance residuals with graph attention and bidirectional LSTM to learn spatio-temporal patterns. A multi-scale module aggregates detection scores from node to network level. On the BATADAL dataset, it reaches $F1=0.979$, showing $3.3$pp gain and high robustness under $15\%$ parameter noise.

Conformal Prediction-Driven Adaptive Sampling for Digital Twins of Water Distribution Networks

Digital Twins (DTs) for Water Distribution Networks (WDNs) require accurate state estimation with limited sensors. Uniform sampling often wastes resources across nodes with different uncertainty. We propose an adaptive framework combining LSTM forecasting and Conformal Prediction (CP) to estimate node-wise uncertainty and focus sensing on the most uncertain points. Marginal CP is used for its low computational cost, suitable for real-time DTs. Experiments on Hanoi, Net3, and CTOWN show 33-34% lower demand error than uniform sampling at 40% coverage and maintain 89.4-90.2% empirical coverage with only 5-10% extra computation.