Graph Attention Networks with Physical Constraints for Anomaly Detection

2026-01-18

AI Summary

This work addresses the unreliability and low interpretability of existing anomaly detection methods in water distribution networks, which often neglect network topology and physical laws. To overcome these limitations, the authors propose a novel approach that integrates residuals derived from mass and energy conservation principles as physics-informed features. For the first time, normalized violations of physical conservation laws are incorporated into a graph attention network, complemented by a bidirectional LSTM to capture spatiotemporal dependencies. A multi-scale module aggregates anomaly scores from individual nodes to the entire network level. Evaluated on the BATADAL dataset, the method achieves an F1 score of 0.979—3.3 percentage points higher than baseline approaches—and demonstrates strong robustness under 15% parameter noise, offering both high interpretability and generalization capability.

Technology Category

• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Machine Learning: Graph-based Machine Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Web Mining and Content Analysis: Web data provenance, reliability, and authenticity
• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments

Abstract

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.

Problem

• anomaly detection
• water distribution systems
• cyber-physical risks
• network topology
• model interpretability

Innovation

• Graph Attention Network
• Physical Constraints
• Anomaly Detection
• Water Distribution Systems
• Conservation Law Residuals