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Graph Attention Networks with Physical Constraints for Anomaly Detection

Mohammadhossein Homaei, Iman Khazrak, Ruben Molano, Andres Caro, Mar Avila

TL;DR

This work proposes a hydraulic-aware graph attention network using normalized conservation law violations as features, which combines mass and energy balance residuals with graph attention and bidirectional LSTM to learn spatio-temporal patterns.

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.

Graph Attention Networks with Physical Constraints for Anomaly Detection

TL;DR

This work proposes a hydraulic-aware graph attention network using normalized conservation law violations as features, which combines mass and energy balance residuals with graph attention and bidirectional LSTM to learn spatio-temporal patterns.

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 , showing pp gain and high robustness under parameter noise.
Paper Structure (23 sections, 8 equations, 4 figures, 5 tables, 2 algorithms)

This paper contains 23 sections, 8 equations, 4 figures, 5 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Problem-Driven Methodology
  4. Problem Formulation and Motivation
  5. PI Data Representation
  6. Spatio-Temporal Detection Core
  7. Training Objective and Explainability
  8. Benchmark Datasets and Multi-Network Validation
  9. Experimental Results
  10. Setup and Baselines
  11. Overall Performance Comparison
  12. Robustness Mechanism Analysis
  13. Generalization: Multi-Network Validation
  14. Ablation and Component Analysis
  15. Robustness Analysis
  16. ...and 8 more sections

Figures (4)

  • Figure 1: Physics-GAT workflow: physics-informed features feed a GAT-BiLSTM core and an adaptive multi-scale fusion that produces node-level anomaly scores.
  • Figure 2: Physics violation heatmap for Attack #3. J42 (red circle) shows peak violation, correctly identifying the attack target.
  • Figure 3: GAT attention flow during Attack #3. High attention weights (crimson arrows) trace the hydraulic path P1→J15→J32→J42.
  • Figure 4: Temporal profile at J42. Mass violation detected immediately (t=1.0h) while energy violation lags by 15 minutes, confirming physical propagation.