# Graph Attention Networks with Physical Constraints for Anomaly Detection

arXiv: https://arxiv.org/abs/2601.12426 · HTML: https://mlsanity.com/paper/2601.12426/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 20 references that are in the map.
- First posted on arXiv 18 Jan 2026.

## Builds on (most cited first, 6 of 6)

- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Explainable Artificial Intelligence (XAI): Concepts, Taxonomies, Opportunities and Challenges toward Responsible AI](https://mlsanity.com/paper/1910.10045/) (2019)
- [Digital Transformation in the Water Distribution System based on the Digital Twins Concept](https://mlsanity.com/paper/2412.06694/) (2024)
- [Causal Digital Twins for Cyber-Physical Security: A Framework for Robust Anomaly Detection in Industrial Control Systems](https://mlsanity.com/paper/2510.09616/) (2025)
- [Large-Scale Multipurpose Benchmark Datasets For Assessing Data-Driven Deep Learning Approaches For Water Distribution Networks](https://mlsanity.com/paper/2404.15386/) (2024)
- [Conformal Prediction-Driven Adaptive Sampling for Digital Water Twins](https://mlsanity.com/paper/2511.05610/) (2025)

## Built on by (most cited first, 1 of 1)

- [Physics-Constrained Digital Twins for Sensor Integrity in Urban Pedestrian Flow: Detecting Stealthy False Data Injection with Conformal Guarantees](https://mlsanity.com/paper/2609.17635/) (2026)

## Abstract (arXiv)

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 3.3pp gain and high robustness under 15% parameter noise.