Choice of Interior Penalty Coefficient for Interior Penalty Discontinuous Galerkin Method for Biot’s System by Employing Machine Learning
Year: 2024
Author: Sanghyun Lee, Teeratorn Kadeethum, Hamidreza M. Nick
International Journal of Numerical Analysis and Modeling, Vol. 21 (2024), Iss. 5 : pp. 764–792
Abstract
This paper uses neural networks and machine learning to study the optimal choice of the interior penalty parameter of the discontinuous Galerkin finite element methods for both the elliptic problems and Biot’s systems. It is crucial to choose the optimal interior penalty parameter, which is not too small or too large for the stability, robustness, and efficiency of the approximated numerical solutions. Both linear regression and nonlinear artificial neural network methods are employed and compared using several numerical experiments to illustrate the capability of our proposed computational framework. This framework is integral to developing automated numerical simulation because it can automatically identify the optimal interior penalty parameter. Real-time feedback could also be implemented to update and improve model accuracy on the fly.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ijnam2024-1031
International Journal of Numerical Analysis and Modeling, Vol. 21 (2024), Iss. 5 : pp. 764–792
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 29
Keywords: Discontinuous Galerkin interior penalty neural networks machine learning finite element methods.
Author Details
Sanghyun Lee Email
Teeratorn Kadeethum Email
Hamidreza M. Nick Email