SOLUTION OF PDES IN COMPUTATIONAL MECHANICS USING PHYSICS INFORMED NEURAL NETWORKS

Abstract

Several techniques are available for solving partial differential equations (PDEs), including Finite Element Methos (FEM), Finite difference Method (FDM) and Physics Informed Neural Networks (PINNs). This Dissertation provides an introduction to Neural networks and how Physics informed Neural network (PINN) is differ from traditional Artificial Neural Network (ANN). It discusses various activation functions such as sigmoid, ReLU, and optimizers such as SGD, AdaGrad, and Adam. Problem associated with Neural network such as underfit, overfit and Exponential and vanishing gradient problem also discussed. After this literature related this in this work are reviewed. We have taken problem related to solid mechanics and solved using PINN. In first, deflection was predicted at different location of beam, simply supported beam, propped cantilever beam and case where PINN was unable to predict the approximate deflection. And in other problem, 2-dimensional, plane stress block was considered, displacement (Primary Variable) and stress field (Secondary variable was considered) were predicted with respect to nodes, (different node sets was considered) and compare with finite element method Solution.