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A comparison of deep learning-based techniques for solving partial differential equations

Obtaining the solutions of high-dimensional partial differential equations (PDEs) seems to be difficult by utilizing the classical numerical methods. Recently, deep neural networks (DNNs) techniques have received special attentions in solving high–dimensional problems in PDEs. In this study, our que...

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Main Authors: Rabiu Bashir Yunus, Nooraini Zainuddin, Afza Shafie, Muhammad Izzatullah Mohd Mustafa, Samsul Ariffin Abdul Karim
Format: Article
Language:English
English
Published: American Institute of Physics Inc. 2024
Subjects:
QA1-939 Mathematics
QC1-75 General
Online Access:https://eprints.ums.edu.my/id/eprint/38814/1/ABSTRACT.pdf
https://eprints.ums.edu.my/id/eprint/38814/2/FULL%20TEXT.pdf
https://eprints.ums.edu.my/id/eprint/38814/
https://doi.org/10.1063/5.0171671
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spelling my.ums.eprints.388142024-06-12T01:32:46Z https://eprints.ums.edu.my/id/eprint/38814/ A comparison of deep learning-based techniques for solving partial differential equations Rabiu Bashir Yunus Nooraini Zainuddin Afza Shafie Muhammad Izzatullah Mohd Mustafa Samsul Ariffin Abdul Karim QA1-939 Mathematics QC1-75 General Obtaining the solutions of high-dimensional partial differential equations (PDEs) seems to be difficult by utilizing the classical numerical methods. Recently, deep neural networks (DNNs) techniques have received special attentions in solving high–dimensional problems in PDEs. In this study, our quest is to investigate some newly introduced data-driven deep learning-based approaches and compare their performance in terms of their efficiency and faster training towards highdimensional PDEs. However, the comparison is carried out based on different activation functions, number of layers and gradient based optimizers. We consider some benchmark problems in our numerical experiments which includes Burgers equation, Diffusion-reaction equation and Allen-Cahn Equations. American Institute of Physics Inc. 2024 Article NonPeerReviewed text en https://eprints.ums.edu.my/id/eprint/38814/1/ABSTRACT.pdf text en https://eprints.ums.edu.my/id/eprint/38814/2/FULL%20TEXT.pdf Rabiu Bashir Yunus and Nooraini Zainuddin and Afza Shafie and Muhammad Izzatullah Mohd Mustafa and Samsul Ariffin Abdul Karim (2024) A comparison of deep learning-based techniques for solving partial differential equations. AIP Conference Proceedings. pp. 1-12. ISSN 0094243X https://doi.org/10.1063/5.0171671
institution Universiti Malaysia Sabah
building UMS Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Malaysia Sabah
content_source UMS Institutional Repository
url_provider http://eprints.ums.edu.my/
language English
English
topic QA1-939 Mathematics
QC1-75 General
spellingShingle QA1-939 Mathematics
QC1-75 General
Rabiu Bashir Yunus
Nooraini Zainuddin
Afza Shafie
Muhammad Izzatullah Mohd Mustafa
Samsul Ariffin Abdul Karim
A comparison of deep learning-based techniques for solving partial differential equations
description Obtaining the solutions of high-dimensional partial differential equations (PDEs) seems to be difficult by utilizing the classical numerical methods. Recently, deep neural networks (DNNs) techniques have received special attentions in solving high–dimensional problems in PDEs. In this study, our quest is to investigate some newly introduced data-driven deep learning-based approaches and compare their performance in terms of their efficiency and faster training towards highdimensional PDEs. However, the comparison is carried out based on different activation functions, number of layers and gradient based optimizers. We consider some benchmark problems in our numerical experiments which includes Burgers equation, Diffusion-reaction equation and Allen-Cahn Equations.
format Article
author Rabiu Bashir Yunus
Nooraini Zainuddin
Afza Shafie
Muhammad Izzatullah Mohd Mustafa
Samsul Ariffin Abdul Karim
author_facet Rabiu Bashir Yunus
Nooraini Zainuddin
Afza Shafie
Muhammad Izzatullah Mohd Mustafa
Samsul Ariffin Abdul Karim
author_sort Rabiu Bashir Yunus
title A comparison of deep learning-based techniques for solving partial differential equations
title_short A comparison of deep learning-based techniques for solving partial differential equations
title_full A comparison of deep learning-based techniques for solving partial differential equations
title_fullStr A comparison of deep learning-based techniques for solving partial differential equations
title_full_unstemmed A comparison of deep learning-based techniques for solving partial differential equations
title_sort comparison of deep learning-based techniques for solving partial differential equations
publisher American Institute of Physics Inc.
publishDate 2024
url https://eprints.ums.edu.my/id/eprint/38814/1/ABSTRACT.pdf
https://eprints.ums.edu.my/id/eprint/38814/2/FULL%20TEXT.pdf
https://eprints.ums.edu.my/id/eprint/38814/
https://doi.org/10.1063/5.0171671
_version_ 1802978352246554624
score 13.214268

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