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Volume 21, Issue 5
Choice of Interior Penalty Coefficient for Interior Penalty Discontinuous Galerkin Method for Biot’s System by Employing Machine Learning

Sanghyun Lee, Teeratorn Kadeethum & Hamidreza M. Nick

DOI: 10.4208/ijnam2024-1031

Int. J. Numer. Anal. Mod., 21 (2024), pp. 764-792.

Published online: 2024-10

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  • 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.

  • Keywords

Discontinuous Galerkin, interior penalty, neural networks, machine learning, finite element methods.

  • AMS Subject Headings

65N12, 65M60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-21-764, author = {Lee , SanghyunKadeethum , Teeratorn and M. Nick , Hamidreza}, title = {Choice of Interior Penalty Coefficient for Interior Penalty Discontinuous Galerkin Method for Biot’s System by Employing Machine Learning}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2024}, volume = {21}, number = {5}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/10.4208/ijnam2024-1031}, url = {http://global-sci.org/intro/article_detail/ijnam/23452.html} }
TY - JOUR T1 - Choice of Interior Penalty Coefficient for Interior Penalty Discontinuous Galerkin Method for Biot’s System by Employing Machine Learning AU - Lee , Sanghyun AU - Kadeethum , Teeratorn AU - M. Nick , Hamidreza JO - International Journal of Numerical Analysis and Modeling VL - 5 SP - 764 EP - 792 PY - 2024 DA - 2024/10 SN - 21 DO - http://doi.org/10.4208/ijnam2024-1031 UR - https://global-sci.org/intro/article_detail/ijnam/23452.html KW - Discontinuous Galerkin, interior penalty, neural networks, machine learning, finite element methods. AB -

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.

Lee , SanghyunKadeethum , Teeratorn and M. Nick , Hamidreza. (2024). Choice of Interior Penalty Coefficient for Interior Penalty Discontinuous Galerkin Method for Biot’s System by Employing Machine Learning. International Journal of Numerical Analysis and Modeling. 21 (5). 764-792. doi:10.4208/ijnam2024-1031
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