Data-Driven Model Reduction and Transfer Operator Approximation

Stefan Klus*, Feliks Nüske, Péter Koltai, Hao Wu, Ioannis Kevrekidis, Christof Schütte, Frank Noé

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

175 Citations (Scopus)

Abstract

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 approximate transfer operators and their eigenvalues, eigenfunctions, and eigenmodes. The goal is to point out similarities and differences between methods developed independently by the dynamical systems, fluid dynamics, and molecular dynamics communities such as time-lagged independent component analysis, dynamic mode decomposition, and their respective generalizations. As a result, extensions and best practices developed for one particular method can be carried over to other related methods.

Original languageEnglish
Pages (from-to)985-1010
Number of pages26
JournalJournal of Nonlinear Science
Volume28
Issue number3
DOIs
Publication statusPublished - Jun 2018

Keywords

  • Data-driven methods
  • Koopman operator
  • Model reduction
  • Perron-Frobenius operator

ASJC Scopus subject areas

  • Modelling and Simulation
  • General Engineering
  • Applied Mathematics

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