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

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

Physica. D, 2020-05, Vol.406, p.132416, Article 132416 [Periódico revisado por pares]

Elsevier B.V

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  • Título:
    Data-driven approximation of the Koopman generator: Model reduction, system identification, and control
  • Autor: Klus, Stefan ; Nüske, Feliks ; Peitz, Sebastian ; Niemann, Jan-Hendrik ; Clementi, Cecilia ; Schütte, Christof
  • Assuntos: Coarse graining ; Control ; Data-driven methods ; Infinitesimal generator ; Koopman operator ; System identification
  • É parte de: Physica. D, 2020-05, Vol.406, p.132416, Article 132416
  • Descrição: 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. •We present a reformulation of standard EDMD to approximate the Koopman generator.•We illustrate how to estimate stochastic differential equations from data.•We show that gEDMD can be used to identify coarse-grained models and for control.
  • Editor: Elsevier B.V
  • Idioma: Inglês
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  • Realização: ABCD-USP USP   Logos de Redes Sociais: Freepik

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