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.
Bibliographical noteKAUST 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.