Heterogeneous graph neural networks enhance pressure estimation in water distribution networks.

Pressure estimation is crucial for efficient operation and management of water distribution networks (WDNs). However, it is often challenged by limited sensor observations. While graph neural networks (GNNs) have been used to improve hydraulic and water quality predictions of WDNs, their reliance on homogeneous graphs oversimplifies the diverse roles and interactions of hydraulic components, resulting in lower performance under dynamic system states. This research introduces a novel heterogeneous graph neural network (HGNN) framework, which models control units such as pumps and valves as distinct nodes while preserving their interactions through additional edge types. Experimental results using C-Town as a benchmark demonstrate that HGNN outperforms GNN in terms of accuracy, robustness, and adaptability, achieving a mean absolute percentage error (MAPE) of 1.88 % and a mean absolute error (MAE) of 1.70 m under a 95 % masking rate. Additionally, this study shows that optimal sensor placement reduces MAE by up to 15 %, and the proposed HGNN framework achieves high computational efficiency, highlighting its effectiveness in WDN analysis and management. This research offers an advanced and transferable approach for WDN pressure estimation, serving as a superior alternative to traditional pressure evaluation models.