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Communication Dans Un Congrès Année : 2022

Multilayer Perceptron-based Surrogate Models for Finite Element Analysis

Résumé

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.

Dates et versions

hal-04347010 , version 1 (15-12-2023)

Identifiants

Citer

Lawson Oliveira Lima, Julien Rosenberger, Esteban Antier, Frederic Magoules. Multilayer Perceptron-based Surrogate Models for Finite Element Analysis. 2022 21st International Symposium on Distributed Computing and Applications for Business Engineering and Science (DCABES), Oct 2022, Chizhou, France. ⟨10.1109/DCABES57229.2022.00045⟩. ⟨hal-04347010⟩
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