Multilayer Perceptron-based Surrogate Models for Finite Element Analysis
Abstract
Many Partial Differential Equations (PDEs) do not have analytical solution, and can only be solved by numerical methods. In this context, Physics-Informed Neural Networks (PINN) have become important in the last decades, since it uses a neural network and physical conditions to approximate any functions. This paper focuses on hypertuning of a PINN, used to solve a PDE. The behavior of the approximated solution when we change the learning rate or the activation function (sigmoid, hyperbolic tangent, GELU, ReLU and ELU) is here analyzed. A comparative study is done to determine the best characteristics in the problem, as well as to find a learning rate that allows fast and satisfactory learning. GELU and hyperbolic tangent activation functions exhibit better performance than other activation functions. A suitable choice of the learning rate results in higher accuracy and faster convergence.
Cite
@article{arxiv.2211.09380,
title = {Multilayer Perceptron-based Surrogate Models for Finite Element Analysis},
author = {Lawson Oliveira Lima and Julien Rosenberger and Esteban Antier and Frederic Magoules},
journal= {arXiv preprint arXiv:2211.09380},
year = {2022}
}