A minimum potential energy based non-local physics-informed deep learning method for solid mechanics

Abstract

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