A Comprehensive Investigation of Physics-Informed Learning in Forward and Inverse Analysis of Elastic and Elastoplastic Footing

Abstract

Physics-informed learning has emerged as a promising approach for solving forward and inverse partial differential equations in engineering practice, but selecting an optimal loss function remains unclear and parameter identification for inverse analysis lacks efficiency. Meanwhile, their values for engineering-scale elastoplastic problems have not been deeply investigated. In this research, a comprehensive comparison between the strong-form collocation point method (CPM) and the deep Ritz method (DRM) based loss functions for both forward and inverse analysis is conducted, and a novel exponential acceleration method is proposed to enlarge the search space of unknown parameters for inverse analysis. By applying these methods to linear elasticity and elastoplasticity footing cases, we found that physics-informed learning equipped with DRM-based loss functions shows more excellent accuracy in forwardly computing displacement but poor accuracy in predicting strain and stress. Physics-informed learning with CPM-based loss functions shows more excellent performance in inverse analysis than their forward-solving ability. The exponential acceleration method largely enhances the efficiency of inverse analysis without sacrificing accuracy. These new findings inspire the future application of physics-informed learning to engineering-scale elastoplastic problems.