Data-driven approximation of the Koopman generator: Model reduction, system identification, and control

Stefan Klus*, Feliks Nüske, Sebastian Peitz, Jan Hendrik Niemann, Cecilia Clementi, Christof Schütte

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

145 Citations (Scopus)


We derive a data-driven method for the approximation of the Koopman generator called gEDMD, which can be regarded as a straightforward extension of EDMD (extended dynamic mode decomposition). This approach is applicable to deterministic and stochastic dynamical systems. It can be used for computing eigenvalues, eigenfunctions, and modes of the generator and for system identification. In addition to learning the governing equations of deterministic systems, which then reduces to SINDy (sparse identification of nonlinear dynamics), it is possible to identify the drift and diffusion terms of stochastic differential equations from data. Moreover, we apply gEDMD to derive coarse-grained models of high-dimensional systems, and also to determine efficient model predictive control strategies. We highlight relationships with other methods and demonstrate the efficacy of the proposed methods using several guiding examples and prototypical molecular dynamics problems.

Original languageEnglish
Article number132416
JournalPhysica D: Nonlinear Phenomena
Publication statusPublished - May 2020


  • Coarse graining
  • Control
  • Data-driven methods
  • Infinitesimal generator
  • Koopman operator
  • System identification

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics


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