Version 1
: Received: 4 February 2021 / Approved: 5 February 2021 / Online: 5 February 2021 (11:36:31 CET)
How to cite:
Adi Pratama, D.; Abu Bakar, M.; Man, M.; Mashuri, M. ANNs-Based Method for Solving Partial Differential Equations : A Survey. Preprints2021, 2021020160. https://doi.org/10.20944/preprints202102.0160.v1
Adi Pratama, D.; Abu Bakar, M.; Man, M.; Mashuri, M. ANNs-Based Method for Solving Partial Differential Equations : A Survey. Preprints 2021, 2021020160. https://doi.org/10.20944/preprints202102.0160.v1
Adi Pratama, D.; Abu Bakar, M.; Man, M.; Mashuri, M. ANNs-Based Method for Solving Partial Differential Equations : A Survey. Preprints2021, 2021020160. https://doi.org/10.20944/preprints202102.0160.v1
APA Style
Adi Pratama, D., Abu Bakar, M., Man, M., & Mashuri, M. (2021). ANNs-Based Method for Solving Partial Differential Equations : A Survey. Preprints. https://doi.org/10.20944/preprints202102.0160.v1
Chicago/Turabian Style
Adi Pratama, D., Mustafa Man and M. Mashuri. 2021 "ANNs-Based Method for Solving Partial Differential Equations : A Survey" Preprints. https://doi.org/10.20944/preprints202102.0160.v1
Abstract
Conventionally, partial differential equations (PDE) problems are solved numerically through discretization process by using finite difference approximations. The algebraic systems generated by this process are then finalized by using an iterative method. Recently, scientists invented a short cut approach, without discretization process, to solve the PDE problems, namely by using machine learning (ML). This is potential to make scientific machine learning as a new sub-field of research. Thus, given the interest in developing ML for solving PDEs, it makes an abundance of an easy-to-use methods that allows researchers to quickly set up and solve problems. In this review paper, we discussed at least three methods for solving high dimensional of PDEs, namely PyDEns, NeuroDiffEq, and Nangs, which are all based on artificial neural networks (ANNs). ANN is one of the methods under ML which proven to be a universal estimator function. Comparison of numerical results presented in solving the classical PDEs such as heat, wave, and Poisson equations, to look at the accuracy and efficiency of the methods. The results showed that the NeuroDiffEq and Nangs algorithms performed better to solve higher dimensional of PDEs than the PyDEns.
Computer Science and Mathematics, Algebra and Number Theory
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
