# Algorithm-Informed Graph Neural Networks for Leakage Detection and Localization in Water Distribution Networks

arXiv: https://arxiv.org/abs/2408.02797 · HTML: https://mlsanity.com/paper/2408.02797/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 51 references that are in the map.
- First posted on arXiv 5 Aug 2024.

## Builds on (most cited first, 25 of 25)

- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Generalizing to Unseen Domains: A Survey on Domain Generalization](https://mlsanity.com/paper/2103.03097/) (2021)
- [How Neural Networks Extrapolate: From Feedforward to Graph Neural Networks](https://mlsanity.com/paper/2009.11848/) (2020)
- [What Can Neural Networks Reason About?](https://mlsanity.com/paper/1905.13211/) (2019)
- [Neural Execution of Graph Algorithms](https://mlsanity.com/paper/1910.10593/) (2019)
- [Neural Algorithmic Reasoning](https://mlsanity.com/paper/2105.02761/) (2021)
- [Graph Neural Networks are Dynamic Programmers](https://mlsanity.com/paper/2203.15544/) (2022)
- [Pointer Graph Networks](https://mlsanity.com/paper/2006.06380/) (2020)
- [Relational inductive bias for physical construction in humans and machines](https://mlsanity.com/paper/1806.01203/) (2018)
- [Neural Algorithmic Reasoning with Causal Regularisation](https://mlsanity.com/paper/2302.10258/) (2023)
- [Towards Better Out-of-Distribution Generalization of Neural Algorithmic Reasoning Tasks](https://mlsanity.com/paper/2211.00692/) (2022)
- [Simulation of Graph Algorithms with Looped Transformers](https://mlsanity.com/paper/2402.01107/) (2024)
- [How to transfer algorithmic reasoning knowledge to learn new algorithms?](https://mlsanity.com/paper/2110.14056/) (2021)
- [Neural Bipartite Matching](https://mlsanity.com/paper/2005.11304/) (2020)
- [SALSA-CLRS: A Sparse and Scalable Benchmark for Algorithmic Reasoning](https://mlsanity.com/paper/2309.12253/) (2023)
- [On the Markov Property of Neural Algorithmic Reasoning: Analyses and Methods](https://mlsanity.com/paper/2403.04929/) (2024)
- [Discrete Neural Algorithmic Reasoning](https://mlsanity.com/paper/2402.11628/) (2024)
- [Reconstructing nodal pressures in water distribution systems with graph neural networks](https://mlsanity.com/paper/2104.13619/) (2021)
- [Learning Graph Algorithms With Recurrent Graph Neural Networks](https://mlsanity.com/paper/2212.04934/) (2022)
- [Learning to Configure Computer Networks with Neural Algorithmic Reasoning](https://mlsanity.com/paper/2211.01980/) (2022)

## Abstract (arXiv)

Detecting and localizing leakages is a significant challenge for the efficient and sustainable management of water distribution networks (WDN). Leveraging the inherent graph structure of WDNs, recent approaches have used graph-based data-driven methods. However, these methods often learn shortcuts that work well with in-distribution data but fail to generalize to out-of-distribution data. To address this limitation and inspired by the perfect generalization ability of classical algorithms, we propose an algorithm-informed graph neural network (AIGNN). Recognizing that WDNs function as flow networks, incorporating max-flow information can be beneficial for inferring pressures. In the proposed framework, we first train AIGNN to emulate the Ford-Fulkerson algorithm for solving max-flow problems. This algorithmic knowledge is then transferred to address the pressure estimation problem in WDNs. Two AIGNNs are deployed, one to reconstruct pressure based on the current measurements, and another to predict pressure based on previous measurements. Leakages are detected and localized by comparing the outputs of the reconstructor and the predictor. By pretraining AIGNNs to reason like algorithms, they are expected to extract more task-relevant and generalizable features. Experimental results demonstrate that the proposed algorithm-informed approach achieves superior results with better generalization ability compared to GNNs that do not incorporate algorithmic knowledge.