Dynamic mode decomposition and its variants

PJ Schmid - Annual Review of Fluid Mechanics, 2022 - annualreviews.org
Dynamic mode decomposition (DMD) is a factorization and dimensionality reduction
technique for data sequences. In its most common form, it processes high-dimensional …

Data-driven model reduction and transfer operator approximation

S Klus, F Nüske, P Koltai, H Wu, I Kevrekidis… - Journal of Nonlinear …, 2018 - Springer
In this review paper, we will present different data-driven dimension reduction techniques for
dynamical systems that are based on transfer operator theory as well as methods to …

Rigorous data‐driven computation of spectral properties of Koopman operators for dynamical systems

MJ Colbrook, A Townsend - Communications on Pure and …, 2024 - Wiley Online Library
Koopman operators are infinite‐dimensional operators that globally linearize nonlinear
dynamical systems, making their spectral information valuable for understanding dynamics …

On the numerical approximation of the Perron-Frobenius and Koopman operator

S Klus, P Koltai, C Schütte - ar**: transport of phase space densities on triangulated surfaces
DJ Chappell, G Tanner, D Löchel… - Proceedings of the …, 2013 - royalsocietypublishing.org
Energy distributions of high-frequency linear wave fields are often modelled in terms of flow
or transport equations with ray dynamics given by a Hamiltonian vector field in phase space …

Nonparametric approximation of conditional expectation operators

M Mollenhauer, P Koltai - arxiv preprint arxiv:2012.12917, 2020 - arxiv.org
Given the joint distribution of two random variables $ X, Y $ on some second countable
locally compact Hausdorff space, we investigate the statistical approximation of the $ L^ 2 …