Academic Journal
A pretraining domain decomposition method using artificial neural networks to solve elliptic PDE boundary value problems.
| Τίτλος: | A pretraining domain decomposition method using artificial neural networks to solve elliptic PDE boundary value problems. |
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| Συγγραφείς: | Seo, Jeong-Kweon |
| Πηγή: | Scientific Reports; 10/14/2022, Vol. 12 Issue 1, p1-16, 16p |
| Θεματικοί όροι: | Domain decomposition methods, Boundary value problems, Partial differential equations, Artificial neural networks, Decomposition method, Machine learning |
| Περίληψη: | 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. [ABSTRACT FROM AUTHOR] |
| Copyright of Scientific Reports is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Βάση Δεδομένων: | Complementary Index |
| FullText | Links: – Type: other Text: Availability: 0 CustomLinks: – Url: https://dx.doi.org/doi:10.1038/s41598-022-18315-4 Name: EDS - Springer Nature Journals (s7799221) Category: fullText Text: View record at Springer |
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| Items | – Name: Title Label: Title Group: Ti Data: A pretraining domain decomposition method using artificial neural networks to solve elliptic PDE boundary value problems. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Seo%2C+Jeong-Kweon%22">Seo, Jeong-Kweon</searchLink> – Name: TitleSource Label: Source Group: Src Data: Scientific Reports; 10/14/2022, Vol. 12 Issue 1, p1-16, 16p – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Domain+decomposition+methods%22">Domain decomposition methods</searchLink><br /><searchLink fieldCode="DE" term="%22Boundary+value+problems%22">Boundary value problems</searchLink><br /><searchLink fieldCode="DE" term="%22Partial+differential+equations%22">Partial differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Artificial+neural+networks%22">Artificial neural networks</searchLink><br /><searchLink fieldCode="DE" term="%22Decomposition+method%22">Decomposition method</searchLink><br /><searchLink fieldCode="DE" term="%22Machine+learning%22">Machine learning</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: 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. [ABSTRACT FROM AUTHOR] – Name: Abstract Label: Group: Ab Data: <i>Copyright of Scientific Reports is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1038/s41598-022-18315-4 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 16 StartPage: 1 Subjects: – SubjectFull: Domain decomposition methods Type: general – SubjectFull: Boundary value problems Type: general – SubjectFull: Partial differential equations Type: general – SubjectFull: Artificial neural networks Type: general – SubjectFull: Decomposition method Type: general – SubjectFull: Machine learning Type: general Titles: – TitleFull: A pretraining domain decomposition method using artificial neural networks to solve elliptic PDE boundary value problems. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Seo, Jeong-Kweon IsPartOfRelationships: – BibEntity: Dates: – D: 14 M: 10 Text: 10/14/2022 Type: published Y: 2022 Identifiers: – Type: issn-print Value: 20452322 Numbering: – Type: volume Value: 12 – Type: issue Value: 1 Titles: – TitleFull: Scientific Reports Type: main |
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