Data-Driven Model Reduction and Transfer Operator Approximation

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

Research output: Contribution to journalArticle

47 Scopus citations

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 (US)
Pages (from-to)985-1010
Number of pages26
JournalJournal of Nonlinear Science
Volume28
Issue number3
DOIs
StatePublished - Jun 1 2018

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Engineering(all)
  • Applied Mathematics

Keywords

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

Fingerprint Dive into the research topics of 'Data-Driven Model Reduction and Transfer Operator Approximation'. Together they form a unique fingerprint.

  • Cite this

    Klus, S., Nüske, F., Koltai, P., Wu, H., Kevrekidis, I., Schütte, C., & Noé, F. (2018). Data-Driven Model Reduction and Transfer Operator Approximation. Journal of Nonlinear Science, 28(3), 985-1010. https://doi.org/10.1007/s00332-017-9437-7