Kernel Principal Component Analysis for Allen-Cahn Equations

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dc.authoridUzunca, Murat/0000-0001-5262-063X
dc.authoridCAKIR, Yusuf/0000-0001-8016-0941
dc.contributor.authorCakir, Yusuf
dc.contributor.authorUzunca, Murat
dc.date.accessioned2025-03-23T19:26:19Z
dc.date.available2025-03-23T19:26:19Z
dc.date.issued2024
dc.departmentSinop Üniversitesi
dc.description.abstractDifferent researchers have analyzed effective computational methods that maintain the precision of Allen-Cahn (AC) equations and their constant security. This article presents a method known as the reduced-order model technique by utilizing kernel principle component analysis (KPCA), a nonlinear variation of traditional principal component analysis (PCA). KPCA is utilized on the data matrix created using discrete solution vectors of the AC equation. In order to achieve discrete solutions, small variations are applied for dividing up extraterrestrial elements, while Kahan's method is used for temporal calculations. Handling the process of backmapping from small-scale space involves utilizing a non-iterative formula rooted in the concept of the multidimensional scaling (MDS) method. Using KPCA, we show that simplified sorting methods preserve the dissipation of the energy structure. The effectiveness of simplified solutions from linear PCA and KPCA, the retention of invariants, and computational speeds are shown through one-, two-, and three-dimensional AC equations.
dc.identifier.doi10.3390/math12213434
dc.identifier.issn2227-7390
dc.identifier.issue21
dc.identifier.scopus2-s2.0-85208440090
dc.identifier.scopusqualityQ1
dc.identifier.urihttps://doi.org/10.3390/math12213434
dc.identifier.urihttps://hdl.handle.net/11486/4684
dc.identifier.volume12
dc.identifier.wosWOS:001351772800001
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherMdpi
dc.relation.ispartofMathematics
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_WOS_20250323
dc.subjectAllen-Cahn equation
dc.subjectkernel principle component analysis
dc.subjectmultidimensional scaling
dc.subjectenergy dissipation
dc.titleKernel Principal Component Analysis for Allen-Cahn Equations
dc.typeArticle

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