Learning physics and temporal dependencies: real-time modeling of water distribution systems via Kolmogorov–Arnold attention networks
Abstract Real-time modeling is vital for the intelligent management of urban water distribution systems (WDSs), enabling proactive decision-making, rapid anomaly detection, and efficient operational control. In comparison with traditional mechanistic simulators, data-driven models offer faster compu...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2025-08-01
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| Series: | npj Clean Water |
| Online Access: | https://doi.org/10.1038/s41545-025-00505-y |
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| _version_ | 1849767333084528640 |
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| author | Zekun Zou Zhihong Long Gang Xu Raziyeh Farmani Tingchao Yu Shipeng Chu |
| author_facet | Zekun Zou Zhihong Long Gang Xu Raziyeh Farmani Tingchao Yu Shipeng Chu |
| author_sort | Zekun Zou |
| collection | DOAJ |
| description | Abstract Real-time modeling is vital for the intelligent management of urban water distribution systems (WDSs), enabling proactive decision-making, rapid anomaly detection, and efficient operational control. In comparison with traditional mechanistic simulators, data-driven models offer faster computation and reduced calibration demands, making them more suitable for real-time applications. However, existing models often accumulate long-term prediction errors and fail to capture the strong temporal dependencies in measured time series. To address these challenges, this study proposes the Kolmogorov–Arnold Attention Network for the real-time modeling of WDSs (KANSA), which combines Kolmogorov–Arnold Networks with attention mechanisms to extract temporal dependency features through bidirectional spatiotemporal processing. Additionally, a multi-equation soft-constraint formulation embeds mass and energy conservation laws into the loss function, mitigating cumulative errors and enhancing physical consistency. Evaluations on a benchmark network and a real-world system demonstrate that KANSA achieves high-accuracy real-time estimation and pattern fidelity while maintaining engineering-grade hydraulic balance. |
| format | Article |
| id | doaj-art-eda8324d24ff4bc7beab9e1e57d90cfa |
| institution | DOAJ |
| issn | 2059-7037 |
| language | English |
| publishDate | 2025-08-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | npj Clean Water |
| spelling | doaj-art-eda8324d24ff4bc7beab9e1e57d90cfa2025-08-20T03:04:16ZengNature Portfolionpj Clean Water2059-70372025-08-018111210.1038/s41545-025-00505-yLearning physics and temporal dependencies: real-time modeling of water distribution systems via Kolmogorov–Arnold attention networksZekun Zou0Zhihong Long1Gang Xu2Raziyeh Farmani3Tingchao Yu4Shipeng Chu5College of Civil Engineering and Architecture, Zhejiang UniversityGuangzhou Water Supply Co. LtdCollege of Civil Engineering and Architecture, Zhejiang UniversityCentre for Water Systems, Department of Engineering, University of Exeter, ExeterCollege of Civil Engineering and Architecture, Zhejiang UniversityCollege of Civil Engineering and Architecture, Zhejiang UniversityAbstract Real-time modeling is vital for the intelligent management of urban water distribution systems (WDSs), enabling proactive decision-making, rapid anomaly detection, and efficient operational control. In comparison with traditional mechanistic simulators, data-driven models offer faster computation and reduced calibration demands, making them more suitable for real-time applications. However, existing models often accumulate long-term prediction errors and fail to capture the strong temporal dependencies in measured time series. To address these challenges, this study proposes the Kolmogorov–Arnold Attention Network for the real-time modeling of WDSs (KANSA), which combines Kolmogorov–Arnold Networks with attention mechanisms to extract temporal dependency features through bidirectional spatiotemporal processing. Additionally, a multi-equation soft-constraint formulation embeds mass and energy conservation laws into the loss function, mitigating cumulative errors and enhancing physical consistency. Evaluations on a benchmark network and a real-world system demonstrate that KANSA achieves high-accuracy real-time estimation and pattern fidelity while maintaining engineering-grade hydraulic balance.https://doi.org/10.1038/s41545-025-00505-y |
| spellingShingle | Zekun Zou Zhihong Long Gang Xu Raziyeh Farmani Tingchao Yu Shipeng Chu Learning physics and temporal dependencies: real-time modeling of water distribution systems via Kolmogorov–Arnold attention networks npj Clean Water |
| title | Learning physics and temporal dependencies: real-time modeling of water distribution systems via Kolmogorov–Arnold attention networks |
| title_full | Learning physics and temporal dependencies: real-time modeling of water distribution systems via Kolmogorov–Arnold attention networks |
| title_fullStr | Learning physics and temporal dependencies: real-time modeling of water distribution systems via Kolmogorov–Arnold attention networks |
| title_full_unstemmed | Learning physics and temporal dependencies: real-time modeling of water distribution systems via Kolmogorov–Arnold attention networks |
| title_short | Learning physics and temporal dependencies: real-time modeling of water distribution systems via Kolmogorov–Arnold attention networks |
| title_sort | learning physics and temporal dependencies real time modeling of water distribution systems via kolmogorov arnold attention networks |
| url | https://doi.org/10.1038/s41545-025-00505-y |
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