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 journalArticlepeer-review

175 Scopus citations


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
Issue number3
StatePublished - Jun 1 2018
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • General Engineering
  • Applied Mathematics


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


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