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

S. Klus, F. Nüske, S. Peitz, J.-H. Niemann, C. Clementi, C. Schütte, Physica D: Nonlinear Phenomena 406 (2020).

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Journal Article | Published | English
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Abstract
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.
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Journal Title
Physica D: Nonlinear Phenomena
Volume
406
Article Number
132416
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Klus S, Nüske F, Peitz S, Niemann J-H, Clementi C, Schütte C. Data-driven approximation of the Koopman generator: Model reduction, system identification, and control. Physica D: Nonlinear Phenomena. 2020;406. doi:10.1016/j.physd.2020.132416
Klus, S., Nüske, F., Peitz, S., Niemann, J.-H., Clementi, C., & Schütte, C. (2020). Data-driven approximation of the Koopman generator: Model reduction, system identification, and control. Physica D: Nonlinear Phenomena, 406. https://doi.org/10.1016/j.physd.2020.132416
@article{Klus_Nüske_Peitz_Niemann_Clementi_Schütte_2020, title={Data-driven approximation of the Koopman generator: Model reduction, system identification, and control}, volume={406}, DOI={10.1016/j.physd.2020.132416}, number={132416}, journal={Physica D: Nonlinear Phenomena}, author={Klus, Stefan and Nüske, Feliks and Peitz, Sebastian and Niemann, Jan-Hendrik and Clementi, Cecilia and Schütte, Christof}, year={2020} }
Klus, Stefan, Feliks Nüske, Sebastian Peitz, Jan-Hendrik Niemann, Cecilia Clementi, and Christof Schütte. “Data-Driven Approximation of the Koopman Generator: Model Reduction, System Identification, and Control.” Physica D: Nonlinear Phenomena 406 (2020). https://doi.org/10.1016/j.physd.2020.132416.
S. Klus, F. Nüske, S. Peitz, J.-H. Niemann, C. Clementi, and C. Schütte, “Data-driven approximation of the Koopman generator: Model reduction, system identification, and control,” Physica D: Nonlinear Phenomena, vol. 406, 2020.
Klus, Stefan, et al. “Data-Driven Approximation of the Koopman Generator: Model Reduction, System Identification, and Control.” Physica D: Nonlinear Phenomena, vol. 406, 132416, 2020, doi:10.1016/j.physd.2020.132416.

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