Solving elastodynamics via physics-informed neural network frequency domain method

Abstract

Despite the fact that physics-informed neural networks (PINN) have been developed rapidly in recent years, their inherent spectral bias makes it difficult to approximate multi-frequency target functions such as the solutions to elastodynamics problems. To address this challenge, this paper proposes a new PINN frequency domain (PINNFD) method on the basis of frequency domain inputs. Fourier features for all frequencies can thus be constructed and embedded in the model, which provides essential support for the PINNFD method to accurately approximate multi-frequency target functions. To validate the effectiveness of the proposed PINNFD method, the proposed method and the traditional method are applied to solve the elastodynamics problem in infinite media under various dynamic point loads, including single-frequency harmonic load, multi-frequency harmonic load, and multi-frequency random load. The results show that although the PINN with embedded Fourier features is able to achieve the simulation of elastodynamics problems under harmonic loads, it fails to solve the problems under multi-frequency random loads. Whereas the proposed PINNFD method achieves better results in all cases of loading conditions, which demonstrates the advancement of the proposed method in solving multi-frequency problems in engineering applications.