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Dergiler / Sinop Üniversitesi Fen Bilimleri Dergisi / 2026 / Cilt: 11 Sayı: 1

Rotasyonlu Termal Sığ Su Denklemi için Çekirdek Temel Bileşen Analizi ile Doğrusal Olmayan Mertebe İndirgenmiş Modelleme

Nonlinear Reduced-Order Modeling of the Rotating Thermal Shallow Water Equation via Kernel Principal Component Analysis

Yusuf Çakır(SINOP UNIVERSITY)0000-0001-8016-0941
Murat Uzunca(SINOP UNIVERSITY)0000-0001-5262-063X
Sayfa
424–440
Yayın Tarihi
2026-06-26
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Önerilen yöntem doğrusal olmayan jeofizik akış modellerinin etkin benzetimi için umut verici bir yaklaşım oluşturmaktadır.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:Bu çalışmada, rotasyonlu termal sığ su denklemi için çekirdek temel bileşen analizi (ÇTBA) tabanlı veriye dayalı doğrusal olmayan bir mertebe indirgenmiş modelleme yaklaşımı geliştirilmiştir.
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Temel Bulgular & Veri:Yüksek boyutlu tam model, denklemlerin uzayda sonlu farklar yöntemi ile ayrıklaştırılması ve zamanda enerji korumalı ortalama vektör alanı yöntemi ile çözülmesi sonucunda elde edilmiştir.
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Sonuç & Katkı:Önerilen yöntem doğrusal olmayan jeofizik akış modellerinin etkin benzetimi için umut verici bir yaklaşım oluşturmaktadır.
🔬Tür:Modelleme & Sayısal Simülasyon
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Rotasyonlu termal sığ su denklemi · çekirdek temel bileşenler analizi · mertebe indirgenmiş modelleme

Özet

Bu çalışmada, rotasyonlu termal sığ su denklemi için çekirdek temel bileşen analizi (ÇTBA) tabanlı veriye dayalı doğrusal olmayan bir mertebe indirgenmiş modelleme yaklaşımı geliştirilmiştir. Yüksek boyutlu tam model, denklemlerin uzayda sonlu farklar yöntemi ile ayrıklaştırılması ve zamanda enerji korumalı ortalama vektör alanı yöntemi ile çözülmesi sonucunda elde edilmiştir. Önerilen yöntem, çözüm manifoldunun doğrusal olmayan düşük boyutlu temsilini elde etmek için ÇTBA kullanmaktadır. ÇTBA yönteminde, çekirdek fonksiyonlar aracılığıyla anlık görüntü verileri örtük olarak yüksek boyutlu bir özellik uzayına taşınmakta ve doğrusal altuzay yöntemlerine kıyasla doğrusal olmayan tutarlı yapılar daha etkin biçimde yakalanabilmektedir. Önerilen yöntem doğrusal olmayan jeofizik akış modellerinin etkin benzetimi için umut verici bir yaklaşım oluşturmaktadır.

Abstract

In this study, a data-driven nonlinear reduced-order modeling framework based on Kernel Principal Component Analysis (KPCA) is developed for the rotating thermal shallow water equation. The high-dimensional full-order model is obtained by discretizing the governing equations in space using finite differences and integrating in time with the energy-preserving average vector field method. The proposed approach employs KPCA to construct a nonlinear low-dimensional representation of the solution manifold, by implicitly mapping the snapshot data into a high-dimensional feature space through kernel functions, and captures nonlinear coherent structures more effectively than the linear subspace methods. The proposed framework is a promising approach for efficient simulation of nonlinear geophysical flow models.

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Bu Makaleye Atıf Yap

Çakır, Y., Uzunca, M. (2026). Rotasyonlu Termal Sığ Su Denklemi için Çekirdek Temel Bileşen Analizi ile Doğrusal Olmayan Mertebe İndirgenmiş Modelleme. Sinop Üniversitesi Fen Bilimleri Dergisi, Cilt: 11 Sayı: 1, 424–440. https://doi.org/10.33484/sinopfbd.1932542

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