Kernel Principal Component Analysis for Allen–Cahn Equations
Yazarlar (2)
Dr. Öğr. Üyesi Yusuf ÇAKIR Sinop Üniversitesi, Türkiye
Prof. Dr. Murat UZUNCA Sinop Üniversitesi, Türkiye
| Makale Türü |
Özgün Makale
(SSCI, AHCI, SCI, SCI-Exp dergilerinde yayınlanan tam makale)
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| Dergi Adı | Mathematics (Q1) | ||
| Dergi ISSN | 2227-7390 Dergi Bilgileri (2024) | ||
| Dergi Tarandığı Indeksler | SCI-Expanded | ||
| Makale Dili | İngilizce | Basım Tarihi | 11-2024 |
| Cilt / Sayı / Sayfa | 12 / 21 / 3434–0 | DOI | 10.3390/math12213434 |
| Makale Linki | http://dx.doi.org/10.3390/math12213434 | ||
| UAK Araştırma Alanları |
Uygulamalı Matematik
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| Özet |
| Different 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. |
| Anahtar Kelimeler |
| Allen–Cahn equation | energy dissipation | kernel principle component analysis | multidimensional scaling |
BM Sürdürülebilir Kalkınma Amaçları
| Atıf Sayıları | |
| Web of Science | 1 |
| Scopus | 1 |
| Google Scholar | 1 |