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math.DS2025
A Data-Driven Framework for Koopman Semigroup Estimation in Stochastic Dynamical Systems
Yuanchao Xu, Kaidi Shao, Isao Ishikawa +3
We present Stochastic Dynamic Mode Decomposition (SDMD), a novel data-driven framework for approximating the Koopman semigroup in stochastic dynamical systems. Unlike existing meth…
math.DS2024★ 4 cited
Koopman operators with intrinsic observables in rigged reproducing kernel Hilbert spaces
Isao Ishikawa, Yuka Hashimoto, Masahiro Ikeda +1
This paper presents a novel approach for estimating the Koopman operator defined on a reproducing kernel Hilbert space (RKHS) and its spectra. We propose an estimation method, what…