A pretraining domain decomposition method using artificial neural networks to solve elliptic PDE boundary value problems

Developing methods of domain decomposition (DDM) has been widely studied in the field of numerical computation to estimate solutions of partial differential equations (PDEs). Several case studies have also reported that it is feasible to use the domain decomposition approach for the application of a...

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Bibliographic Details
Published in:Scientific reports Vol. 12; no. 1; pp. 13939 - 16
Main Author: Seo, Jeong-Kweon
Format: Journal Article
Language:English
Published: London Nature Publishing Group UK 17.08.2022
Nature Publishing Group
Nature Portfolio
Subjects:
639/166
639/705
639/766
Approximation
Boundary value problems
Decomposition
Differential equations
Humanities and Social Sciences
Machine learning
multidisciplinary
Neural networks
Partial differential equations
Science
Science (multidisciplinary)
ISSN:2045-2322, 2045-2322
Online Access:Get full text
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Summary:Developing methods of domain decomposition (DDM) has been widely studied in the field of numerical computation to estimate solutions of partial differential equations (PDEs). Several case studies have also reported that it is feasible to use the domain decomposition approach for the application of artificial neural networks (ANNs) to solve PDEs. In this study, we devised a pretraining scheme called smoothing with a basis reconstruction process on the structure of ANNs and then implemented the classic concept of DDM. The pretraining process that is engaged at the beginning of the training epochs can make the approximation basis become well-posed on the domain so that the quality of the estimated solution is enhanced. We report that such a well-organized pretraining scheme may affect any NN-based PDE solvers as we can speed up the approximation, improve the solution’s smoothness, and so on. Numerical experiments were performed to verify the effectiveness of the proposed DDM method on ANN for estimating solutions of PDEs. Results revealed that this method could be used as a tool for tasks in general machine learning.
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ISSN:2045-2322
2045-2322
DOI:10.1038/s41598-022-18315-4