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arXiv · 2211.09380

Multilayer Perceptron-based Surrogate Models for Finite Element Analysis

Lawson Oliveira Lima·Julien Rosenberger·Esteban Antier·Frederic Magoules
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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.

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Lawson Oliveira Lima, Julien Rosenberger, Esteban Antier, Frederic Magoules. 2022-11-17. Multilayer Perceptron-based Surrogate Models for Finite Element Analysis. https://arxiv.org/abs/2211.09380

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