[{"author":[{"id":"81513","full_name":"Nüske, Feliks","first_name":"Feliks","last_name":"Nüske","orcid":"0000-0003-2444-7889"},{"last_name":"Gelß","first_name":"Patrick","full_name":"Gelß, Patrick"},{"last_name":"Klus","first_name":"Stefan","full_name":"Klus, Stefan"},{"full_name":"Clementi, Cecilia","first_name":"Cecilia","last_name":"Clementi"}],"publication_identifier":{"issn":["0167-2789"]},"title":"Tensor-based computation of metastable and coherent sets","year":"2021","status":"public","date_updated":"2022-01-06T06:56:08Z","publication_status":"published","_id":"24169","language":[{"iso":"eng"}],"article_number":"133018","doi":"10.1016/j.physd.2021.133018","user_id":"81513","citation":{"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>","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>.","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>.","short":"F. Nüske, P. Gelß, S. Klus, C. Clementi, Physica D: Nonlinear Phenomena (2021).","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>.","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>","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} }"},"publication":"Physica D: Nonlinear Phenomena","date_created":"2021-09-12T08:51:24Z","department":[{"_id":"101"}],"type":"journal_article"},{"abstract":[{"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.","lang":"eng"}],"publication":"Physica D: Nonlinear Phenomena","citation":{"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>.","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} }","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>","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.","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>","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>.","short":"S. Klus, F. Nüske, S. Peitz, J.-H. Niemann, C. Clementi, C. Schütte, Physica D: Nonlinear Phenomena 406 (2020)."},"type":"journal_article","department":[{"_id":"101"}],"date_created":"2020-03-13T12:35:40Z","publication_status":"published","date_updated":"2022-01-06T06:52:48Z","intvolume":"       406","status":"public","year":"2020","title":"Data-driven approximation of the Koopman generator: Model reduction, system identification, and control","author":[{"last_name":"Klus","first_name":"Stefan","full_name":"Klus, Stefan"},{"full_name":"Nüske, Feliks","last_name":"Nüske","first_name":"Feliks","orcid":"0000-0003-2444-7889","id":"81513"},{"id":"47427","last_name":"Peitz","orcid":"https://orcid.org/0000-0002-3389-793X","first_name":"Sebastian","full_name":"Peitz, Sebastian"},{"full_name":"Niemann, Jan-Hendrik","last_name":"Niemann","first_name":"Jan-Hendrik"},{"full_name":"Clementi, Cecilia","first_name":"Cecilia","last_name":"Clementi"},{"full_name":"Schütte, Christof","last_name":"Schütte","first_name":"Christof"}],"publication_identifier":{"issn":["0167-2789"]},"user_id":"47427","doi":"10.1016/j.physd.2020.132416","volume":406,"article_number":"132416","language":[{"iso":"eng"}],"_id":"16288"},{"date_updated":"2022-01-06T06:52:53Z","publication_status":"published","title":"Rigorous computation of topological entropy with respect to a finite partition","status":"public","year":"2001","publication_identifier":{"issn":["0167-2789"]},"author":[{"first_name":"Gary","last_name":"Froyland","full_name":"Froyland, Gary"},{"full_name":"Junge, Oliver","last_name":"Junge","first_name":"Oliver"},{"full_name":"Ochs, Gunter","first_name":"Gunter","last_name":"Ochs"}],"doi":"10.1016/s0167-2789(01)00216-0","user_id":"15701","page":"68-84","_id":"16601","language":[{"iso":"eng"}],"publication":"Physica D: Nonlinear Phenomena","citation":{"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} }","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>","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>.","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>.","short":"G. Froyland, O. Junge, G. Ochs, Physica D: Nonlinear Phenomena (2001) 68–84.","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.","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>"},"type":"journal_article","department":[{"_id":"101"}],"date_created":"2020-04-16T06:08:12Z"},{"doi":"10.1016/0167-2789(93)90198-a","user_id":"15701","language":[{"iso":"eng"}],"_id":"16518","page":"66-87","date_updated":"2022-01-06T06:52:52Z","publication_status":"published","publication_identifier":{"issn":["0167-2789"]},"author":[{"full_name":"Barany, Ernest","last_name":"Barany","first_name":"Ernest"},{"first_name":"Michael","last_name":"Dellnitz","full_name":"Dellnitz, Michael"},{"full_name":"Golubitsky, Martin","first_name":"Martin","last_name":"Golubitsky"}],"year":"1993","title":"Detecting the symmetry of attractors","status":"public","department":[{"_id":"101"}],"type":"journal_article","date_created":"2020-04-15T08:02:09Z","citation":{"ieee":"E. Barany, M. Dellnitz, and M. Golubitsky, “Detecting the symmetry of attractors,” <i>Physica D: Nonlinear Phenomena</i>, pp. 66–87, 1993.","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>","short":"E. Barany, M. Dellnitz, M. Golubitsky, Physica D: Nonlinear Phenomena (1993) 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>.","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>.","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} }","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>"},"publication":"Physica D: Nonlinear Phenomena"}]