# Physics-Informed Graph Neural Networks for Water Distribution Systems

arXiv: https://arxiv.org/abs/2403.18570 · HTML: https://mlsanity.com/paper/2403.18570/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 36 references that are in the map.
- First posted on arXiv 27 Mar 2024.

## Builds on (most cited first, 17 of 17)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Self-Normalizing Neural Networks](https://mlsanity.com/paper/1706.02515/) (2017)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [Learning Convolutional Neural Networks for Graphs](https://mlsanity.com/paper/1605.05273/) (2016)
- [DeeperGCN: All You Need to Train Deeper GCNs](https://mlsanity.com/paper/2006.07739/) (2020)
- [Deep Convolutional Networks on Graph-Structured Data](https://mlsanity.com/paper/1506.05163/) (2015)
- [CayleyNets: Graph Convolutional Neural Networks with Complex Rational Spectral Filters](https://mlsanity.com/paper/1705.07664/) (2017)
- [Adaptive Graph Convolutional Neural Networks](https://mlsanity.com/paper/1801.03226/) (2018)
- [Large-Scale Learnable Graph Convolutional Networks](https://mlsanity.com/paper/1808.03965/) (2018)
- [Traffic4cast at NeurIPS 2021 -- Temporal and Spatial Few-Shot Transfer Learning in Gridded Geo-Spatial Processes](https://mlsanity.com/paper/2203.17070/) (2022)
- [Reconstructing nodal pressures in water distribution systems with graph neural networks](https://mlsanity.com/paper/2104.13619/) (2021)
- [Surrogate Neural Networks for Efficient Simulation-based Trajectory Planning Optimization](https://mlsanity.com/paper/2303.17468/) (2023)

## Built on by (most cited first, 9 of 9)

- [Dual-Balancing for Physics-Informed Neural Networks](https://mlsanity.com/paper/2505.11117/) (2025)
- [DiTEC-WDN: A Large-Scale Dataset of Hydraulic Scenarios across Multiple Water Distribution Networks](https://mlsanity.com/paper/2503.17167/) (2025)
- [A Survey of Physics-Informed AI for Complex Urban Systems](https://mlsanity.com/paper/2506.13777/) (2025)
- [DUALFloodGNN: Physics-informed Graph Neural Network for Operational Flood Modeling](https://mlsanity.com/paper/2512.23964/) (2025)
- [A Toolbox for Supporting Research on AI in Water Distribution Networks](https://mlsanity.com/paper/2406.02078/) (2024)
- [WaterAdmin: Orchestrating Community Water Distribution Optimization via AI Agents](https://mlsanity.com/paper/2604.10343/) (2026)
- [Scalable and Robust Physics-Informed Graph Neural Networks for Water Distribution Systems](https://mlsanity.com/paper/2502.12164/) (2025)
- [Interpretable Event Diagnosis in Water Distribution Networks](https://mlsanity.com/paper/2505.07299/) (2025)
- [Verifiable abstention makes AI leak diagnosis accountable in urban water distribution networks](https://mlsanity.com/paper/2608.18836/) (2026)

## Abstract (arXiv)

Water distribution systems (WDS) are an integral part of critical infrastructure which is pivotal to urban development. As 70% of the world's population will likely live in urban environments in 2050, efficient simulation and planning tools for WDS play a crucial role in reaching UN's sustainable developmental goal (SDG) 6 - "Clean water and sanitation for all". In this realm, we propose a novel and efficient machine learning emulator, more precisely, a physics-informed deep learning (DL) model, for hydraulic state estimation in WDS. Using a recursive approach, our model only needs a few graph convolutional neural network (GCN) layers and employs an innovative algorithm based on message passing. Unlike conventional machine learning tasks, the model uses hydraulic principles to infer two additional hydraulic state features in the process of reconstructing the available ground truth feature in an unsupervised manner. To the best of our knowledge, this is the first DL approach to emulate the popular hydraulic simulator EPANET, utilizing no additional information. Like most DL models and unlike the hydraulic simulator, our model demonstrates vastly faster emulation times that do not increase drastically with the size of the WDS. Moreover, we achieve high accuracy on the ground truth and very similar results compared to the hydraulic simulator as demonstrated through experiments on five real-world WDS datasets.