The DOI matches its Crossref record; 55 of the 55 references it cites were found in a registry or an index.
Data-driven approximation of the Koopman generator: Model reduction, system identification, and control
Open accessAbstract
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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Cites
Dynamic mode decomposition of numerical and experimental data
SCHMID, P. J. (2010) · Journal of Fluid Mechanics · doi:10.1017/s0022112010001217 · Cited by 5,915
Discovering governing equations from data by sparse identification of nonlinear dynamical systems
Brunton, S. L., Proctor, J. L., & Kutz, J. N. (2016) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1517384113 · Cited by 4,796
Hamiltonian Systems and Transformation in Hilbert Space
Koopman, B. O. (1931) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.17.5.315 · Cited by 2,383
A Data–Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition
Williams, M. O., Kevrekidis, I. G., & Rowley, C. W. (2015) · Journal of Nonlinear Science · doi:10.1007/s00332-015-9258-5 · Cited by 1,945
Deep learning for universal linear embeddings of nonlinear dynamics
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Nonlinear Model Predictive Control
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Markov models of molecular kinetics: Generation and validation
Prinz, J.-H., Wu, H., Sarich, M., Keller, B., Senne, M., Held, M., Chodera, J. D., Schütte, C., & Noé, F. (2011) · The Journal of Chemical Physics · doi:10.1063/1.3565032 · Cited by 1,275
Self-citationA Multiscale Coarse-Graining Method for Biomolecular Systems
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Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control
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Metadata
- Authors
- Klus, S., Nüske, F., Peitz, S., Niemann, J.-H., Clementi, C., & Schütte, C.
- Venue
- Physica D: Nonlinear Phenomena
- Publisher
- Elsevier BV
- Published
- 2020-05
- Volume
- 406
- Pages
- 132416
- ISSN
- 0167-2789 (ISSN-L)
- OpenAlex
- W3006550916
- Cited by
- 267
- References
- 55
- FWCI
- 13.92
- Type
- journal article
- Language
- en
- Open access
- bronze
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