Application of Fourier feature physics-information neural network in model of pipeline conveying fluid

Abstract

In addressing the intricate dynamic responses of pipeline conveying fluid characterized by spatiotemporal multi-scales and multi-modal contributions, Fourier feature-embedded physics-information neural network (FF-PINN) is proposed. By introducing Fourier feature mapping to decompose the temporal and spatial scale information, FF-PINN precisely captures the relatively low-frequencies on the macroscopic time scale as well as the relatively high-frequencies on the microscopic scale of the pipeline's vibration. This approach significantly overcomes the spectral bias encountered by PINN when learning high-frequency information. To verify the effectiveness and accuracy of this method, the proposed FF-PINN is applied to solve the pipeline conveying fluid model with fixed support at both ends. The relative L2 error between the obtained results and the reference solution is 1.8×10−2, concurrently with a significant reduction in computational time. Additionally, an analysis of hyperparameter σ selection is conducted to evaluate its impact on the performance of FF-PINN, while establishing the correspondence between hyperparameter and eigenvector frequency. The results demonstrate that choosing appropriate hyperparameters empowers FF-PINN to better learn the vibration of specific frequencies, enabling the accurate modeling of pipeline vibrations’ dynamic response. It provides a potent solution for solving spatiotemporal multi-scale complexity problems involving the superposition of high-and low-frequencies.