# Graph Neural Networks for Pressure Estimation in Water Distribution Systems

arXiv: https://arxiv.org/abs/2311.10579 · HTML: https://mlsanity.com/paper/2311.10579/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 99 references that are in the map.
- First posted on arXiv 17 Nov 2023.

## Builds on (most cited first, 30 of 36)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [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)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [RandAugment: Practical automated data augmentation with a reduced search space](https://mlsanity.com/paper/1909.13719/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [How transferable are features in deep neural networks?](https://mlsanity.com/paper/1411.1792/) (2014)
- [Graph Convolutional Neural Networks for Web-Scale Recommender Systems](https://mlsanity.com/paper/1806.01973/) (2018)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [GraphSAINT: Graph Sampling Based Inductive Learning Method](https://mlsanity.com/paper/1907.04931/) (2019)
- [Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological View](https://mlsanity.com/paper/1909.03211/) (2019)
- [Ray: A Distributed Framework for Emerging AI Applications](https://mlsanity.com/paper/1712.05889/) (2017)
- [Empirical Evaluation of Rectified Activations in Convolutional Network](https://mlsanity.com/paper/1505.00853/) (2015)
- [T-GCN: A Temporal Graph ConvolutionalNetwork for Traffic Prediction](https://mlsanity.com/paper/1811.05320/) (2018)
- [Graph Neural Network for Traffic Forecasting: A Survey](https://mlsanity.com/paper/2101.11174/) (2021)
- [Graph neural networks for materials science and chemistry](https://mlsanity.com/paper/2208.09481/) (2022)
- [On Over-Squashing in Message Passing Neural Networks: The Impact of Width, Depth, and Topology](https://mlsanity.com/paper/2302.02941/) (2023)
- [ETA Prediction with Graph Neural Networks in Google Maps](https://mlsanity.com/paper/2108.11482/) (2021)

## Built on by (most cited first, 8 of 8)

- [DiTEC-WDN: A Large-Scale Dataset of Hydraulic Scenarios across Multiple Water Distribution Networks](https://mlsanity.com/paper/2503.17167/) (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)
- [Scalable and Robust Physics-Informed Graph Neural Networks for Water Distribution Systems](https://mlsanity.com/paper/2502.12164/) (2025)
- [A Multivariate Statistical Framework for Detection, Classification and Pre-localization of Anomalies in Water Distribution Networks](https://mlsanity.com/paper/2512.15685/) (2025)
- [The impact of sensor placement on graph-neural-network-based leakage detection](https://mlsanity.com/paper/2603.24076/) (2026)
- [T3R: Deeper Test-Time Adaptation for Graph Neural Networks via Gradient Rotation](https://mlsanity.com/paper/2606.30011/) (2026)
- [Verifiable abstention makes AI leak diagnosis accountable in urban water distribution networks](https://mlsanity.com/paper/2608.18836/) (2026)

## Abstract (arXiv)

Pressure and flow estimation in Water Distribution Networks (WDN) allows water management companies to optimize their control operations. For many years, mathematical simulation tools have been the most common approach to reconstructing an estimate of the WDN hydraulics. However, pure physics-based simulations involve several challenges, e.g. partially observable data, high uncertainty, and extensive manual configuration. Thus, data-driven approaches have gained traction to overcome such limitations. In this work, we combine physics-based modeling and Graph Neural Networks (GNN), a data-driven approach, to address the pressure estimation problem. First, we propose a new data generation method using a mathematical simulation but not considering temporal patterns and including some control parameters that remain untouched in previous works; this contributes to a more diverse training data. Second, our training strategy relies on random sensor placement making our GNN-based estimation model robust to unexpected sensor location changes. Third, a realistic evaluation protocol considers real temporal patterns and additionally injects the uncertainties intrinsic to real-world scenarios. Finally, a multi-graph pre-training strategy allows the model to be reused for pressure estimation in unseen target WDNs. Our GNN-based model estimates the pressure of a large-scale WDN in The Netherlands with a MAE of 1.94mH2O and a MAPE of 7%, surpassing the performance of previous studies. Likewise, it outperformed previous approaches on other WDN benchmarks, showing a reduction of absolute error up to approximately 52% in the best cases.