Work

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

Year: 2016

Type: article

Abstract: Information about the behavior of dynamical systems can oftenbe obtained by analyzing the eigenvalues and corresponding eigenfunctions oflinear operators associated with a dynamical system. Examples of such operatorsare the Perron-Frobenius and the Koopman operator. In this paper, wewill review di erent methods that have been developed over the last decades tocompute nite-dimensional approximations of these in nite-dimensional operators- in particular Ulam's method and Extended Dynamic Mode Decomposition(EDMD) - and highlight the similarities and di erences between theseapproaches. The results will be illustrated using simple stochastic di erentialequations and molecular dynamics examples.

Source: Journal of Computational Dynamics

DOI: 10.3934/jcd.2016003

Authors: Stefan Klus, Péter Koltai, Christof Schütte

Language: English

Topic: Model Reduction and Neural Networks

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: diamond

Funder: Deutsche Forschungsgemeinschaft

Award: G651204332

OpenAlex ID: W2267246336

FWCI: 6.92

Cites: 63

Cited by: 305

Related to: 10