# Spatial Graph Convolution Neural Networks for Water Distribution Systems

arXiv: https://arxiv.org/abs/2211.09587 · HTML: https://mlsanity.com/paper/2211.09587/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 32 references that are in the map.
- First posted on arXiv 17 Nov 2022.

## Builds on (most cited first, 18 of 18)

- [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)
- [A Survey on The Expressive Power of Graph Neural Networks](https://mlsanity.com/paper/2003.04078/) (2020)
- [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)
- [Graph Neural Network and Koopman Models for Learning Networked Dynamics: A Comparative Study on Power Grid Transients Prediction](https://mlsanity.com/paper/2202.08065/) (2022)

## Built on by (most cited first, 3 of 3)

- [Exact Computation of Any-Order Shapley Interactions for Graph Neural Networks](https://mlsanity.com/paper/2501.16944/) (2025)
- [Graph Neural Networks for Pressure Estimation in Water Distribution Systems](https://mlsanity.com/paper/2311.10579/) (2023)
- [Scalable and Robust Physics-Informed Graph Neural Networks for Water Distribution Systems](https://mlsanity.com/paper/2502.12164/) (2025)

## Abstract (arXiv)

We investigate the task of missing value estimation in graphs as given by water distribution systems (WDS) based on sparse signals as a representative machine learning challenge in the domain of critical infrastructure. The underlying graphs have a comparably low node degree and high diameter, while information in the graph is globally relevant, hence graph neural networks face the challenge of long-term dependencies. We propose a specific architecture based on message passing which displays excellent results for a number of benchmark tasks in the WDS domain. Further, we investigate a multi-hop variation, which requires considerably less resources and opens an avenue towards big WDS graphs.