An Overview on Deep Learning Techniques in Solving Partial Differential Equations

Rabiu Bashir Yunus; Samsul Ariffin Abdul Karim; Afza Shafie; Muhammad Izzatullah; Ahmed Kherd; Mohammad Khatim Hasan; Jumat Sulaiman

doi:10.1007/978-3-031-04028-3_4

An Overview on Deep Learning Techniques in Solving Partial Differential Equations

Rabiu Bashir Yunus, Samsul Ariffin Abdul Karim, Afza Shafie, Muhammad Izzatullah, Ahmed Kherd, Mohammad Khatim Hasan, Jumat Sulaiman

Research output: Chapter in Book/Report/Conference proceeding › Chapter

2 Scopus citations

Abstract

Despite great advances in solving partial differential equations (PDEs) using the numerical discretization, some high- dimensional problems with large number of parameters cannot be handled easily. Owing to the rapid growth of accessible data and computing expedients, recent developments in deep learning techniques for the solution of (PDEs) have yielded outstanding results on distinctive problems. In this chapter, we give an overview on diverse deep learning techniques namely; Physics-Informed Neural Networks (PINNs), Int-Deep, BiPDE-Net etc., which are all devised based on Deep Neural Networks (DNNs). We also discuss on several optimization methods to enrich the accuracy of the training and minimize training time.

Original language	English (US)
Title of host publication	Studies in Systems, Decision and Control
Publisher	Springer International Publishing
Pages	37-47
Number of pages	11
ISBN (Print)	9783031040276
DOIs	https://doi.org/10.1007/978-3-031-04028-3_4
State	Published - Oct 13 2022

Bibliographical note

KAUST Repository Item: Exported on 2022-11-03
Acknowledgements: The first author is fully supported by Graduate Research Assistance (GRA) scheme: YUTP: 015LC0-315 (Uncertainty estimation based on quasi-Newton methods for Full Waveform Inversion (FWI)), Universiti Teknologi PTERONAS. The second author is fully supported by Universiti Malaysia Sabah. Special thank you to the Research Management Centre and Faculty of Computing and Informatics, Universiti Malaysia Sabah.

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10.1007/978-3-031-04028-3_4

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title = "An Overview on Deep Learning Techniques in Solving Partial Differential Equations",

abstract = "Despite great advances in solving partial differential equations (PDEs) using the numerical discretization, some high- dimensional problems with large number of parameters cannot be handled easily. Owing to the rapid growth of accessible data and computing expedients, recent developments in deep learning techniques for the solution of (PDEs) have yielded outstanding results on distinctive problems. In this chapter, we give an overview on diverse deep learning techniques namely; Physics-Informed Neural Networks (PINNs), Int-Deep, BiPDE-Net etc., which are all devised based on Deep Neural Networks (DNNs). We also discuss on several optimization methods to enrich the accuracy of the training and minimize training time.",

author = "Yunus, {Rabiu Bashir} and {Abdul Karim}, {Samsul Ariffin} and Afza Shafie and Muhammad Izzatullah and Ahmed Kherd and Hasan, {Mohammad Khatim} and Jumat Sulaiman",

note = "KAUST Repository Item: Exported on 2022-11-03 Acknowledgements: The first author is fully supported by Graduate Research Assistance (GRA) scheme: YUTP: 015LC0-315 (Uncertainty estimation based on quasi-Newton methods for Full Waveform Inversion (FWI)), Universiti Teknologi PTERONAS. The second author is fully supported by Universiti Malaysia Sabah. Special thank you to the Research Management Centre and Faculty of Computing and Informatics, Universiti Malaysia Sabah.",

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doi = "10.1007/978-3-031-04028-3_4",

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AU - Yunus, Rabiu Bashir

AU - Abdul Karim, Samsul Ariffin

AU - Shafie, Afza

AU - Izzatullah, Muhammad

AU - Kherd, Ahmed

AU - Hasan, Mohammad Khatim

AU - Sulaiman, Jumat

N1 - KAUST Repository Item: Exported on 2022-11-03 Acknowledgements: The first author is fully supported by Graduate Research Assistance (GRA) scheme: YUTP: 015LC0-315 (Uncertainty estimation based on quasi-Newton methods for Full Waveform Inversion (FWI)), Universiti Teknologi PTERONAS. The second author is fully supported by Universiti Malaysia Sabah. Special thank you to the Research Management Centre and Faculty of Computing and Informatics, Universiti Malaysia Sabah.

PY - 2022/10/13

Y1 - 2022/10/13

N2 - Despite great advances in solving partial differential equations (PDEs) using the numerical discretization, some high- dimensional problems with large number of parameters cannot be handled easily. Owing to the rapid growth of accessible data and computing expedients, recent developments in deep learning techniques for the solution of (PDEs) have yielded outstanding results on distinctive problems. In this chapter, we give an overview on diverse deep learning techniques namely; Physics-Informed Neural Networks (PINNs), Int-Deep, BiPDE-Net etc., which are all devised based on Deep Neural Networks (DNNs). We also discuss on several optimization methods to enrich the accuracy of the training and minimize training time.

AB - Despite great advances in solving partial differential equations (PDEs) using the numerical discretization, some high- dimensional problems with large number of parameters cannot be handled easily. Owing to the rapid growth of accessible data and computing expedients, recent developments in deep learning techniques for the solution of (PDEs) have yielded outstanding results on distinctive problems. In this chapter, we give an overview on diverse deep learning techniques namely; Physics-Informed Neural Networks (PINNs), Int-Deep, BiPDE-Net etc., which are all devised based on Deep Neural Networks (DNNs). We also discuss on several optimization methods to enrich the accuracy of the training and minimize training time.

UR - http://hdl.handle.net/10754/685382

UR - https://link.springer.com/10.1007/978-3-031-04028-3_4

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SN - 9783031040276

SP - 37

EP - 47

BT - Studies in Systems, Decision and Control

PB - Springer International Publishing

ER -

An Overview on Deep Learning Techniques in Solving Partial Differential Equations

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