Unsupervised Legendre-Galerkin Neural Network for Solving Partial Differential Equations
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Choi, Junho | - |
dc.contributor.author | Kim, Namjung | - |
dc.contributor.author | Hong, Youngjoon | - |
dc.date.accessioned | 2023-05-11T14:40:20Z | - |
dc.date.available | 2023-05-11T14:40:20Z | - |
dc.date.created | 2023-05-11 | - |
dc.date.issued | 2023-02 | - |
dc.identifier.issn | 2169-3536 | - |
dc.identifier.uri | https://scholarworks.bwise.kr/gachon/handle/2020.sw.gachon/87657 | - |
dc.description.abstract | In recent years, machine learning methods have been used to solve partial differential equations (PDEs) and dynamical systems, leading to the development of a new research field called scientific machine learning, which combines techniques such as deep neural networks and statistical learning with classical problems in applied mathematics. In this paper, we present a novel numerical algorithm that uses machine learning and artificial intelligence to solve PDEs. Based on the Legendre-Galerkin framework, we propose an unsupervised machine learning algorithm that learns multiple instances of the solutions for different types of PDEs. Our approach addresses the limitations of both data-driven and physics-based methods. We apply the proposed neural network to general 1D and 2D PDEs with various boundary conditions, as well as convection-dominated singularly perturbed PDEs that exhibit strong boundary layer behavior. | - |
dc.language | 영어 | - |
dc.language.iso | en | - |
dc.publisher | IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC | - |
dc.relation.isPartOf | IEEE ACCESS | - |
dc.title | Unsupervised Legendre-Galerkin Neural Network for Solving Partial Differential Equations | - |
dc.type | Article | - |
dc.type.rims | ART | - |
dc.description.journalClass | 1 | - |
dc.identifier.wosid | 000952580400001 | - |
dc.identifier.doi | 10.1109/ACCESS.2023.3244681 | - |
dc.identifier.bibliographicCitation | IEEE ACCESS, v.11, pp.23433 - 23446 | - |
dc.description.isOpenAccess | Y | - |
dc.identifier.scopusid | 2-s2.0-85149384408 | - |
dc.citation.endPage | 23446 | - |
dc.citation.startPage | 23433 | - |
dc.citation.title | IEEE ACCESS | - |
dc.citation.volume | 11 | - |
dc.contributor.affiliatedAuthor | Kim, Namjung | - |
dc.type.docType | Article | - |
dc.subject.keywordAuthor | Unsupervised learning | - |
dc.subject.keywordAuthor | deep neural network | - |
dc.subject.keywordAuthor | Legendre-Galerkin approximation | - |
dc.subject.keywordAuthor | spectral bias | - |
dc.subject.keywordAuthor | boundary layer | - |
dc.subject.keywordAuthor | singular perturbation | - |
dc.subject.keywordPlus | CONVECTION-DIFFUSION EQUATIONS | - |
dc.subject.keywordPlus | APPROXIMATION | - |
dc.subject.keywordPlus | ALGORITHM | - |
dc.relation.journalResearchArea | Computer Science | - |
dc.relation.journalResearchArea | Engineering | - |
dc.relation.journalResearchArea | Telecommunications | - |
dc.relation.journalWebOfScienceCategory | Computer Science, Information Systems | - |
dc.relation.journalWebOfScienceCategory | Engineering, Electrical & Electronic | - |
dc.relation.journalWebOfScienceCategory | Telecommunications | - |
dc.description.journalRegisteredClass | scie | - |
dc.description.journalRegisteredClass | scopus | - |
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