Poster
Dynamic Mode Decomposition with Reproducing Kernels for Koopman Spectral Analysis
Yoshinobu Kawahara

Mon Dec 5th 06:00 -- 09:30 PM @ Area 5+6+7+8 #109 #None
in Monday Posters »

A spectral analysis of the Koopman operator, which is an infinite dimensional linear operator on an observable, gives a (modal) description of the global behavior of a nonlinear dynamical system without any explicit prior knowledge of its governing equations. In this paper, we consider a spectral analysis of the Koopman operator in a reproducing kernel Hilbert space (RKHS). We propose a modal decomposition algorithm to perform the analysis using finite-length data sequences generated from a nonlinear system. The algorithm is in essence reduced to the calculation of a set of orthogonal bases for the Krylov matrix in RKHS and the eigendecomposition of the projection of the Koopman operator onto the subspace spanned by the bases. The algorithm returns a decomposition of the dynamics into a finite number of modes, and thus it can be thought of as a feature extraction procedure for a nonlinear dynamical system. Therefore, we further consider applications in machine learning using extracted features with the presented analysis. We illustrate the method on the applications using synthetic and real-world data.

Keywords: Time Series Analysis · Spectral Methods · Kernel Methods

Author Information

Yoshinobu Kawahara (Osaka University)

More from the Same Authors