ReLU artificial neural networks for the grid adaptation in finite element method

In this paper, we study the rectified linear unit (ReLU) artificial neural network (ANN) for grid adaptation in finite element method, which is used for solving differential equations (DEs) with initial/boundary condition. Compared with the classical adaptive finite element method (AFEM), ReLU ANN b...

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Bibliographic Details
Published inJournal of physics. Conference series Vol. 1978; no. 1; pp. 12032 - 12039
Main Authors Fu, Xuemei, Chen, Luoping, Wu, Fanyun
Format Journal Article
LanguageEnglish
Published Bristol IOP Publishing 01.07.2021
Subjects
Adaptation
Artificial neural networks
Boundary conditions
Differential equations
Finite element analysis
Finite element method
Neural networks
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ISSN1742-6588
1742-6596
1742-6596
DOI10.1088/1742-6596/1978/1/012032

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Summary:In this paper, we study the rectified linear unit (ReLU) artificial neural network (ANN) for grid adaptation in finite element method, which is used for solving differential equations (DEs) with initial/boundary condition. Compared with the classical adaptive finite element method (AFEM), ReLU ANN based on finite element method can keep the number of grid-points constant but change their relative location. Our numerical experiments show that approximate solutions obtained from the classical finite element method by ReLU ANN are more accurate than those obtained by AFEM.
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ISSN:1742-6588
1742-6596
1742-6596
DOI:10.1088/1742-6596/1978/1/012032