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

By Stefan Klus, Feliks Nuske, Sebastian Peitz, Jan-Hendrik Niemann, Cecilia Clementi, Christof Schutte. Physica A: Statistical Mechanics and its Applications, 2019

310 citations recorded by the source corpus.

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.

Subfields: Aerospace Engineering, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/13216da8e7d3a65502a4a4a93dced3d356963e0d

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Citations in the corpus

Data-driven discovery of Koopman eigenfunctions for control (2017, methodology): “Interestingly, the infinitesimal generator of the Koopman operator may be sparse even when the Koopman operator itself is not [60].”