A study on Physics-Informed Neural Network’s parameters influences in solid mechanics problems.

Resumo

In recent years, Physics-Informed Neural Networks (PINNs) have introduced a novel approach to solving partial differential equations (PDEs) using deep learning techniques. Despite the promising results and rapid advancements in the field, there is a lack of more accurate studies concerning properties related to modeling choices within the deep learning framework, especially, but not exclusively, in solid mechanics problems. In this study, we aim to explore whether the neural network architecture, activation function, optimizer, and sampling method can influence the accuracy of results and training speed for solid mechanics problems. We will focus on elasticity and hyperelasticity problems in 1D, 2D, and 3D dimensions to lay the groundwork for more complex investigations.