---
_id: '24169'
article_number: '133018'
author:
- first_name: Feliks
  full_name: Nüske, Feliks
  id: '81513'
  last_name: Nüske
  orcid: 0000-0003-2444-7889
- first_name: Patrick
  full_name: Gelß, Patrick
  last_name: Gelß
- first_name: Stefan
  full_name: Klus, Stefan
  last_name: Klus
- first_name: Cecilia
  full_name: Clementi, Cecilia
  last_name: Clementi
citation:
  ama: 'Nüske F, Gelß P, Klus S, Clementi C. Tensor-based computation of metastable
    and coherent sets. <i>Physica D: Nonlinear Phenomena</i>. Published online 2021.
    doi:<a href="https://doi.org/10.1016/j.physd.2021.133018">10.1016/j.physd.2021.133018</a>'
  apa: 'Nüske, F., Gelß, P., Klus, S., &#38; Clementi, C. (2021). Tensor-based computation
    of metastable and coherent sets. <i>Physica D: Nonlinear Phenomena</i>, Article
    133018. <a href="https://doi.org/10.1016/j.physd.2021.133018">https://doi.org/10.1016/j.physd.2021.133018</a>'
  bibtex: '@article{Nüske_Gelß_Klus_Clementi_2021, title={Tensor-based computation
    of metastable and coherent sets}, DOI={<a href="https://doi.org/10.1016/j.physd.2021.133018">10.1016/j.physd.2021.133018</a>},
    number={133018}, journal={Physica D: Nonlinear Phenomena}, author={Nüske, Feliks
    and Gelß, Patrick and Klus, Stefan and Clementi, Cecilia}, year={2021} }'
  chicago: 'Nüske, Feliks, Patrick Gelß, Stefan Klus, and Cecilia Clementi. “Tensor-Based
    Computation of Metastable and Coherent Sets.” <i>Physica D: Nonlinear Phenomena</i>,
    2021. <a href="https://doi.org/10.1016/j.physd.2021.133018">https://doi.org/10.1016/j.physd.2021.133018</a>.'
  ieee: 'F. Nüske, P. Gelß, S. Klus, and C. Clementi, “Tensor-based computation of
    metastable and coherent sets,” <i>Physica D: Nonlinear Phenomena</i>, Art. no.
    133018, 2021, doi: <a href="https://doi.org/10.1016/j.physd.2021.133018">10.1016/j.physd.2021.133018</a>.'
  mla: 'Nüske, Feliks, et al. “Tensor-Based Computation of Metastable and Coherent
    Sets.” <i>Physica D: Nonlinear Phenomena</i>, 133018, 2021, doi:<a href="https://doi.org/10.1016/j.physd.2021.133018">10.1016/j.physd.2021.133018</a>.'
  short: 'F. Nüske, P. Gelß, S. Klus, C. Clementi, Physica D: Nonlinear Phenomena
    (2021).'
date_created: 2021-09-12T08:51:24Z
date_updated: 2022-01-06T06:56:08Z
department:
- _id: '101'
doi: 10.1016/j.physd.2021.133018
language:
- iso: eng
publication: 'Physica D: Nonlinear Phenomena'
publication_identifier:
  issn:
  - 0167-2789
publication_status: published
status: public
title: Tensor-based computation of metastable and coherent sets
type: journal_article
user_id: '81513'
year: '2021'
...
---
_id: '16288'
abstract:
- lang: eng
  text: 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.
article_number: '132416'
author:
- first_name: Stefan
  full_name: Klus, Stefan
  last_name: Klus
- first_name: Feliks
  full_name: Nüske, Feliks
  id: '81513'
  last_name: Nüske
  orcid: 0000-0003-2444-7889
- first_name: Sebastian
  full_name: Peitz, Sebastian
  id: '47427'
  last_name: Peitz
  orcid: https://orcid.org/0000-0002-3389-793X
- first_name: Jan-Hendrik
  full_name: Niemann, Jan-Hendrik
  last_name: Niemann
- first_name: Cecilia
  full_name: Clementi, Cecilia
  last_name: Clementi
- first_name: Christof
  full_name: Schütte, Christof
  last_name: Schütte
citation:
  ama: '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. <i>Physica D: Nonlinear Phenomena</i>. 2020;406. doi:<a href="https://doi.org/10.1016/j.physd.2020.132416">10.1016/j.physd.2020.132416</a>'
  apa: 'Klus, S., Nüske, F., Peitz, S., Niemann, J.-H., Clementi, C., &#38; Schütte,
    C. (2020). Data-driven approximation of the Koopman generator: Model reduction,
    system identification, and control. <i>Physica D: Nonlinear Phenomena</i>, <i>406</i>.
    <a href="https://doi.org/10.1016/j.physd.2020.132416">https://doi.org/10.1016/j.physd.2020.132416</a>'
  bibtex: '@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={<a href="https://doi.org/10.1016/j.physd.2020.132416">10.1016/j.physd.2020.132416</a>},
    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} }'
  chicago: '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.” <i>Physica D: Nonlinear
    Phenomena</i> 406 (2020). <a href="https://doi.org/10.1016/j.physd.2020.132416">https://doi.org/10.1016/j.physd.2020.132416</a>.'
  ieee: '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,” <i>Physica D: Nonlinear Phenomena</i>, vol. 406, 2020.'
  mla: 'Klus, Stefan, et al. “Data-Driven Approximation of the Koopman Generator:
    Model Reduction, System Identification, and Control.” <i>Physica D: Nonlinear
    Phenomena</i>, vol. 406, 132416, 2020, doi:<a href="https://doi.org/10.1016/j.physd.2020.132416">10.1016/j.physd.2020.132416</a>.'
  short: 'S. Klus, F. Nüske, S. Peitz, J.-H. Niemann, C. Clementi, C. Schütte, Physica
    D: Nonlinear Phenomena 406 (2020).'
date_created: 2020-03-13T12:35:40Z
date_updated: 2022-01-06T06:52:48Z
department:
- _id: '101'
doi: 10.1016/j.physd.2020.132416
intvolume: '       406'
language:
- iso: eng
publication: 'Physica D: Nonlinear Phenomena'
publication_identifier:
  issn:
  - 0167-2789
publication_status: published
status: public
title: 'Data-driven approximation of the Koopman generator: Model reduction, system
  identification, and control'
type: journal_article
user_id: '47427'
volume: 406
year: '2020'
...
---
_id: '16601'
author:
- first_name: Gary
  full_name: Froyland, Gary
  last_name: Froyland
- first_name: Oliver
  full_name: Junge, Oliver
  last_name: Junge
- first_name: Gunter
  full_name: Ochs, Gunter
  last_name: Ochs
citation:
  ama: 'Froyland G, Junge O, Ochs G. Rigorous computation of topological entropy with
    respect to a finite partition. <i>Physica D: Nonlinear Phenomena</i>. 2001:68-84.
    doi:<a href="https://doi.org/10.1016/s0167-2789(01)00216-0">10.1016/s0167-2789(01)00216-0</a>'
  apa: 'Froyland, G., Junge, O., &#38; Ochs, G. (2001). Rigorous computation of topological
    entropy with respect to a finite partition. <i>Physica D: Nonlinear Phenomena</i>,
    68–84. <a href="https://doi.org/10.1016/s0167-2789(01)00216-0">https://doi.org/10.1016/s0167-2789(01)00216-0</a>'
  bibtex: '@article{Froyland_Junge_Ochs_2001, title={Rigorous computation of topological
    entropy with respect to a finite partition}, DOI={<a href="https://doi.org/10.1016/s0167-2789(01)00216-0">10.1016/s0167-2789(01)00216-0</a>},
    journal={Physica D: Nonlinear Phenomena}, author={Froyland, Gary and Junge, Oliver
    and Ochs, Gunter}, year={2001}, pages={68–84} }'
  chicago: 'Froyland, Gary, Oliver Junge, and Gunter Ochs. “Rigorous Computation of
    Topological Entropy with Respect to a Finite Partition.” <i>Physica D: Nonlinear
    Phenomena</i>, 2001, 68–84. <a href="https://doi.org/10.1016/s0167-2789(01)00216-0">https://doi.org/10.1016/s0167-2789(01)00216-0</a>.'
  ieee: 'G. Froyland, O. Junge, and G. Ochs, “Rigorous computation of topological
    entropy with respect to a finite partition,” <i>Physica D: Nonlinear Phenomena</i>,
    pp. 68–84, 2001.'
  mla: 'Froyland, Gary, et al. “Rigorous Computation of Topological Entropy with Respect
    to a Finite Partition.” <i>Physica D: Nonlinear Phenomena</i>, 2001, pp. 68–84,
    doi:<a href="https://doi.org/10.1016/s0167-2789(01)00216-0">10.1016/s0167-2789(01)00216-0</a>.'
  short: 'G. Froyland, O. Junge, G. Ochs, Physica D: Nonlinear Phenomena (2001) 68–84.'
date_created: 2020-04-16T06:08:12Z
date_updated: 2022-01-06T06:52:53Z
department:
- _id: '101'
doi: 10.1016/s0167-2789(01)00216-0
language:
- iso: eng
page: 68-84
publication: 'Physica D: Nonlinear Phenomena'
publication_identifier:
  issn:
  - 0167-2789
publication_status: published
status: public
title: Rigorous computation of topological entropy with respect to a finite partition
type: journal_article
user_id: '15701'
year: '2001'
...
---
_id: '16518'
author:
- first_name: Ernest
  full_name: Barany, Ernest
  last_name: Barany
- first_name: Michael
  full_name: Dellnitz, Michael
  last_name: Dellnitz
- first_name: Martin
  full_name: Golubitsky, Martin
  last_name: Golubitsky
citation:
  ama: 'Barany E, Dellnitz M, Golubitsky M. Detecting the symmetry of attractors.
    <i>Physica D: Nonlinear Phenomena</i>. 1993:66-87. doi:<a href="https://doi.org/10.1016/0167-2789(93)90198-a">10.1016/0167-2789(93)90198-a</a>'
  apa: 'Barany, E., Dellnitz, M., &#38; Golubitsky, M. (1993). Detecting the symmetry
    of attractors. <i>Physica D: Nonlinear Phenomena</i>, 66–87. <a href="https://doi.org/10.1016/0167-2789(93)90198-a">https://doi.org/10.1016/0167-2789(93)90198-a</a>'
  bibtex: '@article{Barany_Dellnitz_Golubitsky_1993, title={Detecting the symmetry
    of attractors}, DOI={<a href="https://doi.org/10.1016/0167-2789(93)90198-a">10.1016/0167-2789(93)90198-a</a>},
    journal={Physica D: Nonlinear Phenomena}, author={Barany, Ernest and Dellnitz,
    Michael and Golubitsky, Martin}, year={1993}, pages={66–87} }'
  chicago: 'Barany, Ernest, Michael Dellnitz, and Martin Golubitsky. “Detecting the
    Symmetry of Attractors.” <i>Physica D: Nonlinear Phenomena</i>, 1993, 66–87. <a
    href="https://doi.org/10.1016/0167-2789(93)90198-a">https://doi.org/10.1016/0167-2789(93)90198-a</a>.'
  ieee: 'E. Barany, M. Dellnitz, and M. Golubitsky, “Detecting the symmetry of attractors,”
    <i>Physica D: Nonlinear Phenomena</i>, pp. 66–87, 1993.'
  mla: 'Barany, Ernest, et al. “Detecting the Symmetry of Attractors.” <i>Physica
    D: Nonlinear Phenomena</i>, 1993, pp. 66–87, doi:<a href="https://doi.org/10.1016/0167-2789(93)90198-a">10.1016/0167-2789(93)90198-a</a>.'
  short: 'E. Barany, M. Dellnitz, M. Golubitsky, Physica D: Nonlinear Phenomena (1993)
    66–87.'
date_created: 2020-04-15T08:02:09Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1016/0167-2789(93)90198-a
language:
- iso: eng
page: 66-87
publication: 'Physica D: Nonlinear Phenomena'
publication_identifier:
  issn:
  - 0167-2789
publication_status: published
status: public
title: Detecting the symmetry of attractors
type: journal_article
user_id: '15701'
year: '1993'
...