TY - CHAP
T1 - An Overview on Deep Learning Techniques in Solving Partial Differential Equations
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
UR - http://www.scopus.com/inward/record.url?scp=85140227070&partnerID=8YFLogxK
U2 - 10.1007/978-3-031-04028-3_4
DO - 10.1007/978-3-031-04028-3_4
M3 - Chapter
SN - 9783031040276
SP - 37
EP - 47
BT - Studies in Systems, Decision and Control
PB - Springer International Publishing
ER -