Recovering the Forcing Function in Systems with One Degree of Freedom Using ANN and Physics Information

Abstract

In engineering design, oftentimes a system’s dynamic response is known or can be measured, but the source generating these responses is not known. The mathematical problem where the focus is on inferring the source terms of the governing equations from the set of observations is known as an inverse source problem (ISP). ISPs are traditionally solved by optimization techniques with regularization, but in the past few years, there has been a lot of interest in approaching these problems from a deep-learning viewpoint. In this paper, we propose a deep learning approach—infused with physics information—to recover the forcing function (source term) of systems with one degree of freedom from the response data. We test our architecture first to recover smooth forcing functions, and later functions involving abruptly changing gradient and jump discontinuities in the case of a linear system. Finally, we recover the harmonic, the sum of two harmonics, and the gaussian function, in the case of a non-linear system. The results obtained are promising and demonstrate the efficacy of this approach in recovering the forcing functions from the data.