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Transfer learning with graph neural networks for pressure estimation in monitoring-limited water distribution networks.

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Title: Transfer learning with graph neural networks for pressure estimation in monitoring-limited water distribution networks.
Authors: Wang J; Centre for Water Systems, University of Exeter, Exeter EX4 4QF, United Kingdom., Fu G; Centre for Water Systems, University of Exeter, Exeter EX4 4QF, United Kingdom. Electronic address: g.fu@exeter.ac.uk., Savic D; Centre for Water Systems, University of Exeter, Exeter EX4 4QF, United Kingdom; KWR Water Research Institute, Nieuwegein 3430 BB, The Netherlands. Electronic address: d.savic@exeter.ac.uk.
Source: Water research [Water Res] 2025 Dec 01; Vol. 287 (Pt B), pp. 124475. Date of Electronic Publication: 2025 Aug 25.
Publication Type: Journal Article
Language: English
Journal Info: Publisher: Pergamon Press Country of Publication: England NLM ID: 0105072 Publication Model: Print-Electronic Cited Medium: Internet ISSN: 1879-2448 (Electronic) Linking ISSN: 00431354 NLM ISO Abbreviation: Water Res Subsets: MEDLINE
Imprint Name(s): Original Publication: Oxford, Pergamon Press.
MeSH Terms: Neural Networks, Computer* , Water Supply* , Environmental Monitoring*/methods, Graph Neural Networks
Abstract: Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Water distribution networks (WDNs) constitute essential urban infrastructure, yet their monitoring is hindered by limited monitoring conditions. Soft sensing methods have been applied to estimate pressure at unmonitored nodes using the latest deep learning models, however, they rely on large datasets from the same WDNs for training. There is a critical gap in pressure estimation of WDNs under realistic monitoring limitations. This study proposes a Graph Neural Network-based Semi-supervised Transfer Learning (GASTL) approach that estimates node pressures by transferring knowledge between source and target WDNs. GASTL integrates a Heterogeneous Graph Neural Network (HGNN) to extract informative node representations, employs learnable shift parameters for domain adaptation to align source and target distributions, and incorporates Graph Laplacian regularization to enhance spatial consistency and estimation accuracy. The approach is tested on multiple benchmark WDNs, including C-Town, L-Town, and Ky13, under varying sensor numbers and network topology scenarios, and compared against various baseline transfer learning methods. Experimental results demonstrate that GASTL achieves an R² of 0.911 and a Mean Absolute Percentage Error (MAPE) of 9.15 % in Same-topology (e.g., C-Town to C-Town) transfers. In Cross-topology (e.g., L-Town to C-Town) transfers, it attains the same R² of 0.911 and a MAPE of 9.43 %. Further, the study identifies sensor numbers and placement as key factors influencing transfer performance. Notably, the number and location of sensors in the target WDN significantly affect estimation accuracy, whereas topological variations have minimal impact, as they primarily result in shifts in data distribution rather than structural constraints. These findings highlight the potential of transfer learning to improve WDN pressure estimation, offering a scalable and efficient solution for real-world applications.
(Copyright © 2025 The Author(s). Published by Elsevier Ltd.. All rights reserved.)
Contributed Indexing: Keywords: Domain adaptation; Graph neural networks; Semi-supervised learning; Transfer learning; Water distribution networks
Entry Date(s): Date Created: 20250829 Date Completed: 20251021 Latest Revision: 20251021
Update Code: 20251021
DOI: 10.1016/j.watres.2025.124475
PMID: 40882568
Database: MEDLINE
Description
Abstract:Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.<br />Water distribution networks (WDNs) constitute essential urban infrastructure, yet their monitoring is hindered by limited monitoring conditions. Soft sensing methods have been applied to estimate pressure at unmonitored nodes using the latest deep learning models, however, they rely on large datasets from the same WDNs for training. There is a critical gap in pressure estimation of WDNs under realistic monitoring limitations. This study proposes a Graph Neural Network-based Semi-supervised Transfer Learning (GASTL) approach that estimates node pressures by transferring knowledge between source and target WDNs. GASTL integrates a Heterogeneous Graph Neural Network (HGNN) to extract informative node representations, employs learnable shift parameters for domain adaptation to align source and target distributions, and incorporates Graph Laplacian regularization to enhance spatial consistency and estimation accuracy. The approach is tested on multiple benchmark WDNs, including C-Town, L-Town, and Ky13, under varying sensor numbers and network topology scenarios, and compared against various baseline transfer learning methods. Experimental results demonstrate that GASTL achieves an R² of 0.911 and a Mean Absolute Percentage Error (MAPE) of 9.15 % in Same-topology (e.g., C-Town to C-Town) transfers. In Cross-topology (e.g., L-Town to C-Town) transfers, it attains the same R² of 0.911 and a MAPE of 9.43 %. Further, the study identifies sensor numbers and placement as key factors influencing transfer performance. Notably, the number and location of sensors in the target WDN significantly affect estimation accuracy, whereas topological variations have minimal impact, as they primarily result in shifts in data distribution rather than structural constraints. These findings highlight the potential of transfer learning to improve WDN pressure estimation, offering a scalable and efficient solution for real-world applications.<br /> (Copyright © 2025 The Author(s). Published by Elsevier Ltd.. All rights reserved.)
ISSN:1879-2448
DOI:10.1016/j.watres.2025.124475