Spectral physics-informed neural network for transient pipe flow simulation.

Accurate wave propagation models are essential for effective monitoring and automated localization in water supply pipelines. The recently-established Physics-Informed Neural Networks (PINNs) can enhance the wave analysis and reduce uncertainties by integrating mathematical models with sensor data. However, the application of PINN in modelling transient waves remains limited to the time domain, though frequency domain models are preferred for system identification due to their sensitivity to anomalies. This paper develops a PINN-based water hammer model in the frequency domain referred to as Physics-Informed Complex-Valued Neural Network (PICVNN) to enhance the wave prediction for monitoring and assessment applications. Results indicate that the proposed model can effectively reconstruct transient pressures generated using analytical solutions, even in the face of uncertainties including input parameters, mathematical models, and unknown leaks. PICVNN is also compared with two benchmark models of classical complex valued neural network (CVNN) with the same and a doubled number of observation points. PICVNN is found to outperform both CVNN models in terms of accuracy. Unfortunately, this accuracy comes at a cost as PICVNN requires a significantly longer training time than the classical CVNN. Regardless, the developed PICVNN model serves as a reliable signal fusion tool, effectively integrating diverse sensor data to enhance accuracy and reliability.