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 proceedingChapter

1 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 languageEnglish (US)
Title of host publicationStudies in Systems, Decision and Control
PublisherSpringer International Publishing
Pages37-47
Number of pages11
ISBN (Print)9783031040276
DOIs
StatePublished - 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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