A Minimum Potential Energy-Based Nonlocal Physics-Informed Deep Learning Method for Solid Mechanics

Abstract Although success is achieved by physics-informed neural networks (PINNs) as a deep learning solver in many fields, they face some challenges when solving solid mechanics problems. The most notable challenges include the neural network mapping of discontinuous field functions and the time-consuming of training PINNs. To tackle these challenges, this article proposes a minimum potential energy-based nonlocal physics-informed deep learning method (MPE-nPINNs), instead of relying on physical constraints expressed in strong form partial differential equations (PDEs). Additionally, we redesign the neural network structure by integrating peridynamic damage features as additional inputs, which can enhance the ability of the networks to describe the discontinuous field and reduce the size of the networks. We evaluate the training efficiency of the proposed method in problems of solid mechanics through comparative examples, and we verify the effectiveness of incorporating peridynamic damage features into optimizing the network structure. The numerical results indicate that the MPE-nPINNs method exhibits superior convergence speed and effectively characterizes discontinuous field functions with fewer number of hyperparameters of neural networks. This study has significant importance in enhancing the generalization ability of physics-informed neural networks and expediting optimization processes.