4 papers
Diffusion Maps Kernel Ridge Regression
John Harlim, Daning Huang, Jiwoo Song
In this paper, we study kernel ridge regression using the data-driven diffusion maps (DM) kernel, which is constructed through algebraic manipulations of the diffusion maps algorit…
Learning solution operator of dynamical systems with diffusion maps kernel ridge regression
Jiwoo Song, Daning Huang, John Harlim
In this work, we propose a simple kernel ridge regression (KRR) framework with a dynamic-aware validation strategy for long-term prediction of complex dynamical systems. By employi…
Global Description of Flutter Dynamics via Koopman Theory
Jiwoo Song, Daning Huang
This paper presents a novel parametrization approach for aeroelastic systems utilizing Koopman theory, specifically leveraging the Koopman Bilinear Form (KBF) model. To address the…
Modal Analysis of Spatiotemporal Data via Multivariate Gaussian Process Regression
Jiwoo Song, Daning Huang
Modal analysis has become an essential tool to understand the coherent structure of complex flows. The classical modal analysis methods, such as dynamic mode decomposition (DMD) an…