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

Stefan Klus, Péter Koltai, Christof Schütte

Research output: Contribution to journalArticlepeer-review

160 Citations (Scopus)

Abstract

Information about the behavior of dynamical systems can often be obtained by analyzing the eigenvalues and corresponding eigenfunctions of linear operators associated with a dynamical system. Examples of such operators are the Perron-Frobenius and the Koopman operator. In this paper, we will review different methods that have been developed over the last decades to compute finite-dimensional approximations of these infinite-dimensional operators - in particular Ulam's method and Extended Dynamic Mode Decomposition (EDMD) - and highlight the similarities and differences between these approaches. The results will be illustrated using simple stochastic differential equations and molecular dynamics examples.

Original languageEnglish
Pages (from-to)51-79
Number of pages29
JournalJournal of Computational Dynamics
Volume3
Issue number1
DOIs
Publication statusPublished - Jan 2016

Keywords

  • Extended dynamic mode decomposition
  • Galerkin methods
  • Koopman operator
  • Perron-Frobenius operator
  • Transfer operator
  • Ulam's method

ASJC Scopus subject areas

  • Computational Mechanics
  • Computational Mathematics

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