Learning physics and temporal dependencies: real-time modeling of water distribution systems via Kolmogorov–Arnold attention networks

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.