A Hybrid Model Coupling Data and Hydraulic Transient Laws for Water Distribution Systems

Abstract The physics‐informed neural network (PINN) method has been applied to solve water hammer equations in pipeline systems due to its ability of seamlessly integrate measurement data with conservation laws, offering advantages over traditional numerical method. However, existing PINN approaches require multiple neural networks to construct composite models for complex water distribution systems (WDS). This situation treats nodal information as boundary condition or labeled data during training, leading to a weaker robustness and a high demand for data. To address these issues, a hybrid water hammer model based on eXtended Physics‐Informed Neural Networks for WDS (WDS‐XPINN) is developed in this study. Unlike the standard PINN, WDS‐XPINN incorporates the nodal mechanistic model directly into the loss function, enabling to synchronously train a unified neural network jointly through sparse augmented measurement data for pipeline system. Additionally, an adaptive weights method is introduced to improve model robustness by balancing the contributions of flowrates and pressures. The proposed WDS‐XPINN is evaluated in two case studies: a series pipeline system with different operational events and noise perturbation, as well as a topological structure with looped and branched pipe. According to the simulation results and uncertainty analysis, the WDS‐XPINN model demonstrates its excellent capacity of modeling fluid transient accurately in pipeline system, even without exact operational conditions or true pipe parameters.