A meshless Runge-Kutta-based Physics-Informed Neural Network framework for structural vibration analysis

Abstract

In recent years, Physics-Informed Neural Networks (PINN) have emerged as powerful meshless numerical methods for solving partial differential equations (PDEs) in engineering and science, including the field of structural vibration. However, PINN struggles due to the spectral bias when the target PDEs exhibit high-frequency features. In this work, a meshless Runge-Kutta-based PINN (R-KPINN) framework for structural vibration modelling is proposed for the first time. In the framework, the meshless features of traditional PINN are retained while applying Runge-Kutta (R-K) time integration to discretise the temporal domain, thereby reducing computational demands and enhancing temporal flexibility. Besides, the proposed R-KPINN allows for segmental training of PINN, reducing the dimensionality of the structural vibration problems and offering accurate solutions to relatively high-frequency functions. Through numerical examples including free, damped, and forced vibration of Euler-Bernoulli beams, the proposed framework provides effective and precise solutions for predicting the responses of structures. In summary, the proposed R-KPINN framework provides a flexible, efficient, and interpretable meshless method for solving structural vibration problems with state-of-the-art PINN techniques.