An Overview on Deep Learning Techniques in Solving Partial Differential Equations

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. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.