[{"date_updated":"2023-03-17T15:55:33Z","oa":"1","author":[{"first_name":"Manuel","full_name":"Schaller, Manuel","last_name":"Schaller"},{"full_name":"Worthmann, Karl","last_name":"Worthmann","first_name":"Karl"},{"full_name":"Philipp, Friedrich","last_name":"Philipp","first_name":"Friedrich"},{"first_name":"Sebastian","last_name":"Peitz","orcid":"0000-0002-3389-793X","full_name":"Peitz, Sebastian","id":"47427"},{"last_name":"Nüske","orcid":"0000-0003-2444-7889","id":"81513","full_name":"Nüske, Feliks","first_name":"Feliks"}],"volume":56,"main_file_link":[{"open_access":"1","url":"https://www.sciencedirect.com/science/article/pii/S2405896323002173/pdf?md5=164ee9a0343a1bd0e0b9ac4187e44b77&pid=1-s2.0-S2405896323002173-main.pdf"}],"doi":"10.1016/j.ifacol.2023.02.029","conference":{"name":"12th IFAC Symposium on Nonlinear Control Systems (NOLCOS)"},"publication_status":"published","citation":{"apa":"Schaller, M., Worthmann, K., Philipp, F., Peitz, S., &#38; Nüske, F. (2023). Towards reliable data-based optimal and predictive control using extended DMD. <i>IFAC-PapersOnLine</i>, <i>56</i>(1), 169–174. <a href=\"https://doi.org/10.1016/j.ifacol.2023.02.029\">https://doi.org/10.1016/j.ifacol.2023.02.029</a>","mla":"Schaller, Manuel, et al. “Towards Reliable Data-Based Optimal and Predictive Control Using Extended DMD.” <i>IFAC-PapersOnLine</i>, vol. 56, no. 1, 2023, pp. 169–74, doi:<a href=\"https://doi.org/10.1016/j.ifacol.2023.02.029\">10.1016/j.ifacol.2023.02.029</a>.","short":"M. Schaller, K. Worthmann, F. Philipp, S. Peitz, F. Nüske, in: IFAC-PapersOnLine, 2023, pp. 169–174.","bibtex":"@inproceedings{Schaller_Worthmann_Philipp_Peitz_Nüske_2023, title={Towards reliable data-based optimal and predictive control using extended DMD}, volume={56}, DOI={<a href=\"https://doi.org/10.1016/j.ifacol.2023.02.029\">10.1016/j.ifacol.2023.02.029</a>}, number={1}, booktitle={IFAC-PapersOnLine}, author={Schaller, Manuel and Worthmann, Karl and Philipp, Friedrich and Peitz, Sebastian and Nüske, Feliks}, year={2023}, pages={169–174} }","chicago":"Schaller, Manuel, Karl Worthmann, Friedrich Philipp, Sebastian Peitz, and Feliks Nüske. “Towards Reliable Data-Based Optimal and Predictive Control Using Extended DMD.” In <i>IFAC-PapersOnLine</i>, 56:169–74, 2023. <a href=\"https://doi.org/10.1016/j.ifacol.2023.02.029\">https://doi.org/10.1016/j.ifacol.2023.02.029</a>.","ieee":"M. Schaller, K. Worthmann, F. Philipp, S. Peitz, and F. Nüske, “Towards reliable data-based optimal and predictive control using extended DMD,” in <i>IFAC-PapersOnLine</i>, 2023, vol. 56, no. 1, pp. 169–174, doi: <a href=\"https://doi.org/10.1016/j.ifacol.2023.02.029\">10.1016/j.ifacol.2023.02.029</a>.","ama":"Schaller M, Worthmann K, Philipp F, Peitz S, Nüske F. Towards reliable data-based optimal and predictive control using extended DMD. In: <i>IFAC-PapersOnLine</i>. Vol 56. ; 2023:169-174. doi:<a href=\"https://doi.org/10.1016/j.ifacol.2023.02.029\">10.1016/j.ifacol.2023.02.029</a>"},"intvolume":"        56","page":"169-174","_id":"30125","user_id":"47427","department":[{"_id":"655"}],"type":"conference","status":"public","date_created":"2022-02-25T17:14:58Z","title":"Towards reliable data-based optimal and predictive control using extended DMD","issue":"1","year":"2023","external_id":{"arxiv":["2202.09084"]},"language":[{"iso":"eng"}],"publication":"IFAC-PapersOnLine","abstract":[{"lang":"eng","text":"We present an approach for guaranteed constraint satisfaction by means of data-based optimal control, where the model is unknown and has to be obtained from measurement data. To this end, we utilize the Koopman framework and an eDMD-based bilinear surrogate modeling approach for control systems to show an error bound on predicted observables, i.e., functions of the state. This result is then applied to the constraints of the optimal control problem to show that satisfaction of tightened constraints in the purely data-based surrogate model implies constraint satisfaction for the original system."}]},{"status":"public","abstract":[{"lang":"eng","text":"The Koopman operator has become an essential tool for data-driven approximation of dynamical (control) systems in recent years, e.g., via extended dynamic mode decomposition. Despite its popularity, convergence results and, in particular, error bounds are still quite scarce. In this paper, we derive probabilistic bounds for the approximation error and the prediction error depending on the number of training data points; for both ordinary and stochastic differential equations. Moreover, we extend our analysis to nonlinear control-affine systems using either ergodic trajectories or i.i.d.\r\nsamples. Here, we exploit the linearity of the Koopman generator to obtain a bilinear system and, thus, circumvent the curse of dimensionality since we do not autonomize the system by augmenting the state by the control inputs. To the\r\nbest of our knowledge, this is the first finite-data error analysis in the stochastic and/or control setting. Finally, we demonstrate the effectiveness of the proposed approach by comparing it with state-of-the-art techniques showing its superiority whenever state and control are coupled."}],"type":"journal_article","publication":"Journal of Nonlinear Science","language":[{"iso":"eng"}],"article_number":"14","user_id":"47427","department":[{"_id":"101"},{"_id":"655"}],"_id":"23428","citation":{"chicago":"Nüske, Feliks, Sebastian Peitz, Friedrich Philipp, Manuel Schaller, and Karl Worthmann. “Finite-Data Error Bounds for Koopman-Based Prediction and Control.” <i>Journal of Nonlinear Science</i> 33 (2023). <a href=\"https://doi.org/10.1007/s00332-022-09862-1\">https://doi.org/10.1007/s00332-022-09862-1</a>.","ieee":"F. Nüske, S. Peitz, F. Philipp, M. Schaller, and K. Worthmann, “Finite-data error bounds for Koopman-based prediction and control,” <i>Journal of Nonlinear Science</i>, vol. 33, Art. no. 14, 2023, doi: <a href=\"https://doi.org/10.1007/s00332-022-09862-1\">10.1007/s00332-022-09862-1</a>.","ama":"Nüske F, Peitz S, Philipp F, Schaller M, Worthmann K. Finite-data error bounds for Koopman-based prediction and control. <i>Journal of Nonlinear Science</i>. 2023;33. doi:<a href=\"https://doi.org/10.1007/s00332-022-09862-1\">10.1007/s00332-022-09862-1</a>","apa":"Nüske, F., Peitz, S., Philipp, F., Schaller, M., &#38; Worthmann, K. (2023). Finite-data error bounds for Koopman-based prediction and control. <i>Journal of Nonlinear Science</i>, <i>33</i>, Article 14. <a href=\"https://doi.org/10.1007/s00332-022-09862-1\">https://doi.org/10.1007/s00332-022-09862-1</a>","short":"F. Nüske, S. Peitz, F. Philipp, M. Schaller, K. Worthmann, Journal of Nonlinear Science 33 (2023).","mla":"Nüske, Feliks, et al. “Finite-Data Error Bounds for Koopman-Based Prediction and Control.” <i>Journal of Nonlinear Science</i>, vol. 33, 14, 2023, doi:<a href=\"https://doi.org/10.1007/s00332-022-09862-1\">10.1007/s00332-022-09862-1</a>.","bibtex":"@article{Nüske_Peitz_Philipp_Schaller_Worthmann_2023, title={Finite-data error bounds for Koopman-based prediction and control}, volume={33}, DOI={<a href=\"https://doi.org/10.1007/s00332-022-09862-1\">10.1007/s00332-022-09862-1</a>}, number={14}, journal={Journal of Nonlinear Science}, author={Nüske, Feliks and Peitz, Sebastian and Philipp, Friedrich and Schaller, Manuel and Worthmann, Karl}, year={2023} }"},"intvolume":"        33","year":"2023","publication_status":"published","main_file_link":[{"open_access":"1","url":"https://link.springer.com/content/pdf/10.1007/s00332-022-09862-1.pdf"}],"doi":"10.1007/s00332-022-09862-1","title":"Finite-data error bounds for Koopman-based prediction and control","author":[{"first_name":"Feliks","last_name":"Nüske","orcid":"0000-0003-2444-7889","id":"81513","full_name":"Nüske, Feliks"},{"id":"47427","full_name":"Peitz, Sebastian","last_name":"Peitz","orcid":"0000-0002-3389-793X","first_name":"Sebastian"},{"first_name":"Friedrich","full_name":"Philipp, Friedrich","last_name":"Philipp"},{"first_name":"Manuel","last_name":"Schaller","full_name":"Schaller, Manuel"},{"first_name":"Karl","full_name":"Worthmann, Karl","last_name":"Worthmann"}],"date_created":"2021-08-17T12:25:09Z","volume":33,"date_updated":"2023-08-24T07:50:12Z","oa":"1"},{"abstract":[{"text":"Koopman operator theory has been successfully applied to problems from various research areas such as fluid dynamics, molecular dynamics, climate science, engineering, and biology. Applications include detecting metastable or coherent sets, coarse-graining, system identification, and control. There is an intricate connection between dynamical systems driven by stochastic differential equations and quantum mechanics. In this paper, we compare the ground-state transformation and Nelson's stochastic mechanics and demonstrate how data-driven methods developed for the approximation of the Koopman operator can be used to analyze quantum physics problems. Moreover, we exploit the relationship between Schrödinger operators and stochastic control problems to show that modern data-driven methods for stochastic control can be used to solve the stationary or imaginary-time Schrödinger equation. Our findings open up a new avenue towards solving Schrödinger's equation using recently developed tools from data science.","lang":"eng"}],"publication":"Journal of Physics A: Mathematical and Theoretical","language":[{"iso":"eng"}],"external_id":{"arxiv":["2201.12062"]},"year":"2022","issue":"31","title":"Koopman analysis of quantum systems","date_created":"2022-01-31T09:49:40Z","publisher":"IOP Publishing Ltd.","status":"public","type":"journal_article","user_id":"47427","department":[{"_id":"655"},{"_id":"101"}],"_id":"29673","citation":{"ieee":"S. Klus, F. Nüske, and S. Peitz, “Koopman analysis of quantum systems,” <i>Journal of Physics A: Mathematical and Theoretical</i>, vol. 55, no. 31, p. 314002, 2022, doi: <a href=\"https://doi.org/10.1088/1751-8121/ac7d22\">10.1088/1751-8121/ac7d22</a>.","chicago":"Klus, Stefan, Feliks Nüske, and Sebastian Peitz. “Koopman Analysis of Quantum Systems.” <i>Journal of Physics A: Mathematical and Theoretical</i> 55, no. 31 (2022): 314002. <a href=\"https://doi.org/10.1088/1751-8121/ac7d22\">https://doi.org/10.1088/1751-8121/ac7d22</a>.","ama":"Klus S, Nüske F, Peitz S. Koopman analysis of quantum systems. <i>Journal of Physics A: Mathematical and Theoretical</i>. 2022;55(31):314002. doi:<a href=\"https://doi.org/10.1088/1751-8121/ac7d22\">10.1088/1751-8121/ac7d22</a>","apa":"Klus, S., Nüske, F., &#38; Peitz, S. (2022). Koopman analysis of quantum systems. <i>Journal of Physics A: Mathematical and Theoretical</i>, <i>55</i>(31), 314002. <a href=\"https://doi.org/10.1088/1751-8121/ac7d22\">https://doi.org/10.1088/1751-8121/ac7d22</a>","bibtex":"@article{Klus_Nüske_Peitz_2022, title={Koopman analysis of quantum systems}, volume={55}, DOI={<a href=\"https://doi.org/10.1088/1751-8121/ac7d22\">10.1088/1751-8121/ac7d22</a>}, number={31}, journal={Journal of Physics A: Mathematical and Theoretical}, publisher={IOP Publishing Ltd.}, author={Klus, Stefan and Nüske, Feliks and Peitz, Sebastian}, year={2022}, pages={314002} }","mla":"Klus, Stefan, et al. “Koopman Analysis of Quantum Systems.” <i>Journal of Physics A: Mathematical and Theoretical</i>, vol. 55, no. 31, IOP Publishing Ltd., 2022, p. 314002, doi:<a href=\"https://doi.org/10.1088/1751-8121/ac7d22\">10.1088/1751-8121/ac7d22</a>.","short":"S. Klus, F. Nüske, S. Peitz, Journal of Physics A: Mathematical and Theoretical 55 (2022) 314002."},"intvolume":"        55","page":"314002","publication_status":"published","main_file_link":[{"open_access":"1","url":"https://iopscience.iop.org/article/10.1088/1751-8121/ac7d22/pdf"}],"doi":"10.1088/1751-8121/ac7d22","author":[{"first_name":"Stefan","full_name":"Klus, Stefan","last_name":"Klus"},{"first_name":"Feliks","id":"81513","full_name":"Nüske, Feliks","last_name":"Nüske","orcid":"0000-0003-2444-7889"},{"first_name":"Sebastian","orcid":"0000-0002-3389-793X","last_name":"Peitz","id":"47427","full_name":"Peitz, Sebastian"}],"volume":55,"oa":"1","date_updated":"2022-07-18T14:26:41Z"},{"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>","short":"F. Nüske, P. Gelß, S. Klus, C. Clementi, Physica D: Nonlinear Phenomena (2021).","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} }","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>","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>."},"year":"2021","publication_status":"published","publication_identifier":{"issn":["0167-2789"]},"doi":"10.1016/j.physd.2021.133018","title":"Tensor-based computation of metastable and coherent sets","date_created":"2021-09-12T08:51:24Z","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"},{"last_name":"Klus","full_name":"Klus, Stefan","first_name":"Stefan"},{"first_name":"Cecilia","full_name":"Clementi, Cecilia","last_name":"Clementi"}],"date_updated":"2022-01-06T06:56:08Z","status":"public","type":"journal_article","publication":"Physica D: Nonlinear Phenomena","language":[{"iso":"eng"}],"article_number":"133018","user_id":"81513","department":[{"_id":"101"}],"_id":"24169"},{"date_created":"2021-09-12T08:52:57Z","author":[{"full_name":"Klus, Stefan","last_name":"Klus","first_name":"Stefan"},{"first_name":"Patrick","last_name":"Gelß","full_name":"Gelß, Patrick"},{"id":"81513","full_name":"Nüske, Feliks","last_name":"Nüske","orcid":"0000-0003-2444-7889","first_name":"Feliks"},{"last_name":"Noé","full_name":"Noé, Frank","first_name":"Frank"}],"date_updated":"2022-01-06T06:56:08Z","doi":"10.1088/2632-2153/ac14ad","title":"Symmetric and antisymmetric kernels for machine learning problems in quantum physics and chemistry","publication_identifier":{"issn":["2632-2153"]},"publication_status":"published","citation":{"ama":"Klus S, Gelß P, Nüske F, Noé F. Symmetric and antisymmetric kernels for machine learning problems in quantum physics and chemistry. <i>Machine Learning: Science and Technology</i>. Published online 2021. doi:<a href=\"https://doi.org/10.1088/2632-2153/ac14ad\">10.1088/2632-2153/ac14ad</a>","ieee":"S. Klus, P. Gelß, F. Nüske, and F. Noé, “Symmetric and antisymmetric kernels for machine learning problems in quantum physics and chemistry,” <i>Machine Learning: Science and Technology</i>, Art. no. 045016, 2021, doi: <a href=\"https://doi.org/10.1088/2632-2153/ac14ad\">10.1088/2632-2153/ac14ad</a>.","chicago":"Klus, Stefan, Patrick Gelß, Feliks Nüske, and Frank Noé. “Symmetric and Antisymmetric Kernels for Machine Learning Problems in Quantum Physics and Chemistry.” <i>Machine Learning: Science and Technology</i>, 2021. <a href=\"https://doi.org/10.1088/2632-2153/ac14ad\">https://doi.org/10.1088/2632-2153/ac14ad</a>.","apa":"Klus, S., Gelß, P., Nüske, F., &#38; Noé, F. (2021). Symmetric and antisymmetric kernels for machine learning problems in quantum physics and chemistry. <i>Machine Learning: Science and Technology</i>, Article 045016. <a href=\"https://doi.org/10.1088/2632-2153/ac14ad\">https://doi.org/10.1088/2632-2153/ac14ad</a>","bibtex":"@article{Klus_Gelß_Nüske_Noé_2021, title={Symmetric and antisymmetric kernels for machine learning problems in quantum physics and chemistry}, DOI={<a href=\"https://doi.org/10.1088/2632-2153/ac14ad\">10.1088/2632-2153/ac14ad</a>}, number={045016}, journal={Machine Learning: Science and Technology}, author={Klus, Stefan and Gelß, Patrick and Nüske, Feliks and Noé, Frank}, year={2021} }","short":"S. Klus, P. Gelß, F. Nüske, F. Noé, Machine Learning: Science and Technology (2021).","mla":"Klus, Stefan, et al. “Symmetric and Antisymmetric Kernels for Machine Learning Problems in Quantum Physics and Chemistry.” <i>Machine Learning: Science and Technology</i>, 045016, 2021, doi:<a href=\"https://doi.org/10.1088/2632-2153/ac14ad\">10.1088/2632-2153/ac14ad</a>."},"year":"2021","department":[{"_id":"101"}],"user_id":"81513","_id":"24170","language":[{"iso":"eng"}],"article_number":"045016","publication":"Machine Learning: Science and Technology","type":"journal_article","status":"public"},{"publication_identifier":{"issn":["1099-4300"]},"publication_status":"published","citation":{"ama":"Nüske F, Koltai P, Boninsegna L, Clementi C. Spectral Properties of Effective Dynamics from Conditional Expectations. <i>Entropy</i>. 2021. doi:<a href=\"https://doi.org/10.3390/e23020134\">10.3390/e23020134</a>","chicago":"Nüske, Feliks, Péter Koltai, Lorenzo Boninsegna, and Cecilia Clementi. “Spectral Properties of Effective Dynamics from Conditional Expectations.” <i>Entropy</i>, 2021. <a href=\"https://doi.org/10.3390/e23020134\">https://doi.org/10.3390/e23020134</a>.","ieee":"F. Nüske, P. Koltai, L. Boninsegna, and C. Clementi, “Spectral Properties of Effective Dynamics from Conditional Expectations,” <i>Entropy</i>, 2021.","bibtex":"@article{Nüske_Koltai_Boninsegna_Clementi_2021, title={Spectral Properties of Effective Dynamics from Conditional Expectations}, DOI={<a href=\"https://doi.org/10.3390/e23020134\">10.3390/e23020134</a>}, number={134}, journal={Entropy}, author={Nüske, Feliks and Koltai, Péter and Boninsegna, Lorenzo and Clementi, Cecilia}, year={2021} }","short":"F. Nüske, P. Koltai, L. Boninsegna, C. Clementi, Entropy (2021).","mla":"Nüske, Feliks, et al. “Spectral Properties of Effective Dynamics from Conditional Expectations.” <i>Entropy</i>, 134, 2021, doi:<a href=\"https://doi.org/10.3390/e23020134\">10.3390/e23020134</a>.","apa":"Nüske, F., Koltai, P., Boninsegna, L., &#38; Clementi, C. (2021). Spectral Properties of Effective Dynamics from Conditional Expectations. <i>Entropy</i>. <a href=\"https://doi.org/10.3390/e23020134\">https://doi.org/10.3390/e23020134</a>"},"year":"2021","author":[{"first_name":"Feliks","last_name":"Nüske","orcid":"0000-0003-2444-7889","id":"81513","full_name":"Nüske, Feliks"},{"last_name":"Koltai","full_name":"Koltai, Péter","first_name":"Péter"},{"full_name":"Boninsegna, Lorenzo","last_name":"Boninsegna","first_name":"Lorenzo"},{"last_name":"Clementi","full_name":"Clementi, Cecilia","first_name":"Cecilia"}],"date_created":"2021-04-28T18:07:56Z","oa":"1","date_updated":"2022-01-06T06:55:16Z","doi":"10.3390/e23020134","main_file_link":[{"url":"https://www.mdpi.com/1099-4300/23/2/134","open_access":"1"}],"title":"Spectral Properties of Effective Dynamics from Conditional Expectations","publication":"Entropy","type":"journal_article","status":"public","abstract":[{"text":"<jats:p>The reduction of high-dimensional systems to effective models on a smaller set of variables is an essential task in many areas of science. For stochastic dynamics governed by diffusion processes, a general procedure to find effective equations is the conditioning approach. In this paper, we are interested in the spectrum of the generator of the resulting effective dynamics, and how it compares to the spectrum of the full generator. We prove a new relative error bound in terms of the eigenfunction approximation error for reversible systems. We also present numerical examples indicating that, if Kramers–Moyal (KM) type approximations are used to compute the spectrum of the reduced generator, it seems largely insensitive to the time window used for the KM estimators. We analyze the implications of these observations for systems driven by underdamped Langevin dynamics, and show how meaningful effective dynamics can be defined in this setting.</jats:p>","lang":"eng"}],"department":[{"_id":"101"}],"user_id":"81513","_id":"21820","language":[{"iso":"eng"}],"article_number":"134"},{"status":"public","abstract":[{"text":"<jats:p>Many dimensionality and model reduction techniques rely on estimating dominant eigenfunctions of associated dynamical operators from data. Important examples include the Koopman operator and its generator, but also the Schrödinger operator. We propose a kernel-based method for the approximation of differential operators in reproducing kernel Hilbert spaces and show how eigenfunctions can be estimated by solving auxiliary matrix eigenvalue problems. The resulting algorithms are applied to molecular dynamics and quantum chemistry examples. Furthermore, we exploit that, under certain conditions, the Schrödinger operator can be transformed into a Kolmogorov backward operator corresponding to a drift-diffusion process and vice versa. This allows us to apply methods developed for the analysis of high-dimensional stochastic differential equations to quantum mechanical systems.</jats:p>","lang":"eng"}],"type":"journal_article","publication":"Entropy","language":[{"iso":"eng"}],"article_number":"722","user_id":"81513","department":[{"_id":"101"}],"_id":"21819","citation":{"mla":"Klus, Stefan, et al. “Kernel-Based Approximation of the Koopman Generator and Schrödinger Operator.” <i>Entropy</i>, 722, 2020, doi:<a href=\"https://doi.org/10.3390/e22070722\">10.3390/e22070722</a>.","bibtex":"@article{Klus_Nüske_Hamzi_2020, title={Kernel-Based Approximation of the Koopman Generator and Schrödinger Operator}, DOI={<a href=\"https://doi.org/10.3390/e22070722\">10.3390/e22070722</a>}, number={722}, journal={Entropy}, author={Klus, Stefan and Nüske, Feliks and Hamzi, Boumediene}, year={2020} }","short":"S. Klus, F. Nüske, B. Hamzi, Entropy (2020).","apa":"Klus, S., Nüske, F., &#38; Hamzi, B. (2020). Kernel-Based Approximation of the Koopman Generator and Schrödinger Operator. <i>Entropy</i>. <a href=\"https://doi.org/10.3390/e22070722\">https://doi.org/10.3390/e22070722</a>","chicago":"Klus, Stefan, Feliks Nüske, and Boumediene Hamzi. “Kernel-Based Approximation of the Koopman Generator and Schrödinger Operator.” <i>Entropy</i>, 2020. <a href=\"https://doi.org/10.3390/e22070722\">https://doi.org/10.3390/e22070722</a>.","ieee":"S. Klus, F. Nüske, and B. Hamzi, “Kernel-Based Approximation of the Koopman Generator and Schrödinger Operator,” <i>Entropy</i>, 2020.","ama":"Klus S, Nüske F, Hamzi B. Kernel-Based Approximation of the Koopman Generator and Schrödinger Operator. <i>Entropy</i>. 2020. doi:<a href=\"https://doi.org/10.3390/e22070722\">10.3390/e22070722</a>"},"year":"2020","publication_status":"published","publication_identifier":{"issn":["1099-4300"]},"main_file_link":[{"open_access":"1","url":"https://www.mdpi.com/1099-4300/22/7/722"}],"doi":"10.3390/e22070722","title":"Kernel-Based Approximation of the Koopman Generator and Schrödinger Operator","author":[{"last_name":"Klus","full_name":"Klus, Stefan","first_name":"Stefan"},{"first_name":"Feliks","orcid":"0000-0003-2444-7889","last_name":"Nüske","full_name":"Nüske, Feliks","id":"81513"},{"first_name":"Boumediene","last_name":"Hamzi","full_name":"Hamzi, Boumediene"}],"date_created":"2021-04-28T18:06:35Z","date_updated":"2022-01-06T06:55:16Z","oa":"1"},{"publication_identifier":{"issn":["0167-2789"]},"publication_status":"published","intvolume":"       406","citation":{"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>","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).","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>","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."},"year":"2020","volume":406,"date_created":"2020-03-13T12:35:40Z","author":[{"first_name":"Stefan","full_name":"Klus, Stefan","last_name":"Klus"},{"first_name":"Feliks","id":"81513","full_name":"Nüske, Feliks","orcid":"0000-0003-2444-7889","last_name":"Nüske"},{"orcid":"https://orcid.org/0000-0002-3389-793X","last_name":"Peitz","id":"47427","full_name":"Peitz, Sebastian","first_name":"Sebastian"},{"first_name":"Jan-Hendrik","last_name":"Niemann","full_name":"Niemann, Jan-Hendrik"},{"first_name":"Cecilia","last_name":"Clementi","full_name":"Clementi, Cecilia"},{"first_name":"Christof","full_name":"Schütte, Christof","last_name":"Schütte"}],"date_updated":"2022-01-06T06:52:48Z","doi":"10.1016/j.physd.2020.132416","title":"Data-driven approximation of the Koopman generator: Model reduction, system identification, and control","publication":"Physica D: Nonlinear Phenomena","type":"journal_article","status":"public","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."}],"department":[{"_id":"101"}],"user_id":"47427","_id":"16288","language":[{"iso":"eng"}],"article_number":"132416"},{"language":[{"iso":"eng"}],"extern":"1","article_number":"044116","user_id":"81513","department":[{"_id":"101"}],"_id":"21944","status":"public","type":"journal_article","publication":"The Journal of Chemical Physics","doi":"10.1063/1.5100131","title":"Coarse-graining molecular systems by spectral matching","author":[{"last_name":"Nüske","orcid":"0000-0003-2444-7889","full_name":"Nüske, Feliks","id":"81513","first_name":"Feliks"},{"first_name":"Lorenzo","last_name":"Boninsegna","full_name":"Boninsegna, Lorenzo"},{"full_name":"Clementi, Cecilia","last_name":"Clementi","first_name":"Cecilia"}],"date_created":"2021-04-30T17:01:13Z","date_updated":"2022-01-06T06:55:20Z","citation":{"ama":"Nüske F, Boninsegna L, Clementi C. Coarse-graining molecular systems by spectral matching. <i>The Journal of Chemical Physics</i>. 2019. doi:<a href=\"https://doi.org/10.1063/1.5100131\">10.1063/1.5100131</a>","chicago":"Nüske, Feliks, Lorenzo Boninsegna, and Cecilia Clementi. “Coarse-Graining Molecular Systems by Spectral Matching.” <i>The Journal of Chemical Physics</i>, 2019. <a href=\"https://doi.org/10.1063/1.5100131\">https://doi.org/10.1063/1.5100131</a>.","ieee":"F. Nüske, L. Boninsegna, and C. Clementi, “Coarse-graining molecular systems by spectral matching,” <i>The Journal of Chemical Physics</i>, 2019.","apa":"Nüske, F., Boninsegna, L., &#38; Clementi, C. (2019). Coarse-graining molecular systems by spectral matching. <i>The Journal of Chemical Physics</i>. <a href=\"https://doi.org/10.1063/1.5100131\">https://doi.org/10.1063/1.5100131</a>","mla":"Nüske, Feliks, et al. “Coarse-Graining Molecular Systems by Spectral Matching.” <i>The Journal of Chemical Physics</i>, 044116, 2019, doi:<a href=\"https://doi.org/10.1063/1.5100131\">10.1063/1.5100131</a>.","bibtex":"@article{Nüske_Boninsegna_Clementi_2019, title={Coarse-graining molecular systems by spectral matching}, DOI={<a href=\"https://doi.org/10.1063/1.5100131\">10.1063/1.5100131</a>}, number={044116}, journal={The Journal of Chemical Physics}, author={Nüske, Feliks and Boninsegna, Lorenzo and Clementi, Cecilia}, year={2019} }","short":"F. Nüske, L. Boninsegna, C. Clementi, The Journal of Chemical Physics (2019)."},"year":"2019","publication_status":"published","publication_identifier":{"issn":["0021-9606","1089-7690"]}},{"year":"2018","page":"2771-2783","citation":{"mla":"Litzinger, Florian, et al. “Rapid Calculation of Molecular Kinetics Using Compressed Sensing.” <i>Journal of Chemical Theory and Computation</i>, 2018, pp. 2771–83, doi:<a href=\"https://doi.org/10.1021/acs.jctc.8b00089\">10.1021/acs.jctc.8b00089</a>.","short":"F. Litzinger, L. Boninsegna, H. Wu, F. Nüske, R. Patel, R. Baraniuk, F. Noé, C. Clementi, Journal of Chemical Theory and Computation (2018) 2771–2783.","bibtex":"@article{Litzinger_Boninsegna_Wu_Nüske_Patel_Baraniuk_Noé_Clementi_2018, title={Rapid Calculation of Molecular Kinetics Using Compressed Sensing}, DOI={<a href=\"https://doi.org/10.1021/acs.jctc.8b00089\">10.1021/acs.jctc.8b00089</a>}, journal={Journal of Chemical Theory and Computation}, author={Litzinger, Florian and Boninsegna, Lorenzo and Wu, Hao and Nüske, Feliks and Patel, Raajen and Baraniuk, Richard and Noé, Frank and Clementi, Cecilia}, year={2018}, pages={2771–2783} }","apa":"Litzinger, F., Boninsegna, L., Wu, H., Nüske, F., Patel, R., Baraniuk, R., … Clementi, C. (2018). Rapid Calculation of Molecular Kinetics Using Compressed Sensing. <i>Journal of Chemical Theory and Computation</i>, 2771–2783. <a href=\"https://doi.org/10.1021/acs.jctc.8b00089\">https://doi.org/10.1021/acs.jctc.8b00089</a>","ieee":"F. Litzinger <i>et al.</i>, “Rapid Calculation of Molecular Kinetics Using Compressed Sensing,” <i>Journal of Chemical Theory and Computation</i>, pp. 2771–2783, 2018.","chicago":"Litzinger, Florian, Lorenzo Boninsegna, Hao Wu, Feliks Nüske, Raajen Patel, Richard Baraniuk, Frank Noé, and Cecilia Clementi. “Rapid Calculation of Molecular Kinetics Using Compressed Sensing.” <i>Journal of Chemical Theory and Computation</i>, 2018, 2771–83. <a href=\"https://doi.org/10.1021/acs.jctc.8b00089\">https://doi.org/10.1021/acs.jctc.8b00089</a>.","ama":"Litzinger F, Boninsegna L, Wu H, et al. Rapid Calculation of Molecular Kinetics Using Compressed Sensing. <i>Journal of Chemical Theory and Computation</i>. 2018:2771-2783. doi:<a href=\"https://doi.org/10.1021/acs.jctc.8b00089\">10.1021/acs.jctc.8b00089</a>"},"publication_identifier":{"issn":["1549-9618","1549-9626"]},"publication_status":"published","title":"Rapid Calculation of Molecular Kinetics Using Compressed Sensing","doi":"10.1021/acs.jctc.8b00089","date_updated":"2022-01-06T06:55:20Z","date_created":"2021-04-30T16:58:07Z","author":[{"first_name":"Florian","last_name":"Litzinger","full_name":"Litzinger, Florian"},{"first_name":"Lorenzo","full_name":"Boninsegna, Lorenzo","last_name":"Boninsegna"},{"last_name":"Wu","full_name":"Wu, Hao","first_name":"Hao"},{"full_name":"Nüske, Feliks","id":"81513","orcid":"0000-0003-2444-7889","last_name":"Nüske","first_name":"Feliks"},{"last_name":"Patel","full_name":"Patel, Raajen","first_name":"Raajen"},{"first_name":"Richard","last_name":"Baraniuk","full_name":"Baraniuk, Richard"},{"last_name":"Noé","full_name":"Noé, Frank","first_name":"Frank"},{"first_name":"Cecilia","last_name":"Clementi","full_name":"Clementi, Cecilia"}],"status":"public","publication":"Journal of Chemical Theory and Computation","type":"journal_article","extern":"1","language":[{"iso":"eng"}],"_id":"21940","department":[{"_id":"101"}],"user_id":"81513"},{"status":"public","type":"journal_article","publication":"Journal of Nonlinear Science","language":[{"iso":"eng"}],"extern":"1","user_id":"81513","department":[{"_id":"101"}],"_id":"21941","citation":{"ieee":"S. Klus <i>et al.</i>, “Data-Driven Model Reduction and Transfer Operator Approximation,” <i>Journal of Nonlinear Science</i>, pp. 985–1010, 2018.","chicago":"Klus, Stefan, Feliks Nüske, Péter Koltai, Hao Wu, Ioannis Kevrekidis, Christof Schütte, and Frank Noé. “Data-Driven Model Reduction and Transfer Operator Approximation.” <i>Journal of Nonlinear Science</i>, 2018, 985–1010. <a href=\"https://doi.org/10.1007/s00332-017-9437-7\">https://doi.org/10.1007/s00332-017-9437-7</a>.","ama":"Klus S, Nüske F, Koltai P, et al. Data-Driven Model Reduction and Transfer Operator Approximation. <i>Journal of Nonlinear Science</i>. 2018:985-1010. doi:<a href=\"https://doi.org/10.1007/s00332-017-9437-7\">10.1007/s00332-017-9437-7</a>","short":"S. Klus, F. Nüske, P. Koltai, H. Wu, I. Kevrekidis, C. Schütte, F. Noé, Journal of Nonlinear Science (2018) 985–1010.","bibtex":"@article{Klus_Nüske_Koltai_Wu_Kevrekidis_Schütte_Noé_2018, title={Data-Driven Model Reduction and Transfer Operator Approximation}, DOI={<a href=\"https://doi.org/10.1007/s00332-017-9437-7\">10.1007/s00332-017-9437-7</a>}, journal={Journal of Nonlinear Science}, author={Klus, Stefan and Nüske, Feliks and Koltai, Péter and Wu, Hao and Kevrekidis, Ioannis and Schütte, Christof and Noé, Frank}, year={2018}, pages={985–1010} }","mla":"Klus, Stefan, et al. “Data-Driven Model Reduction and Transfer Operator Approximation.” <i>Journal of Nonlinear Science</i>, 2018, pp. 985–1010, doi:<a href=\"https://doi.org/10.1007/s00332-017-9437-7\">10.1007/s00332-017-9437-7</a>.","apa":"Klus, S., Nüske, F., Koltai, P., Wu, H., Kevrekidis, I., Schütte, C., &#38; Noé, F. (2018). Data-Driven Model Reduction and Transfer Operator Approximation. <i>Journal of Nonlinear Science</i>, 985–1010. <a href=\"https://doi.org/10.1007/s00332-017-9437-7\">https://doi.org/10.1007/s00332-017-9437-7</a>"},"page":"985-1010","year":"2018","publication_status":"published","publication_identifier":{"issn":["0938-8974","1432-1467"]},"doi":"10.1007/s00332-017-9437-7","title":"Data-Driven Model Reduction and Transfer Operator Approximation","date_created":"2021-04-30T16:59:03Z","author":[{"full_name":"Klus, Stefan","last_name":"Klus","first_name":"Stefan"},{"first_name":"Feliks","full_name":"Nüske, Feliks","id":"81513","orcid":"0000-0003-2444-7889","last_name":"Nüske"},{"first_name":"Péter","full_name":"Koltai, Péter","last_name":"Koltai"},{"full_name":"Wu, Hao","last_name":"Wu","first_name":"Hao"},{"first_name":"Ioannis","last_name":"Kevrekidis","full_name":"Kevrekidis, Ioannis"},{"first_name":"Christof","full_name":"Schütte, Christof","last_name":"Schütte"},{"first_name":"Frank","last_name":"Noé","full_name":"Noé, Frank"}],"date_updated":"2022-01-06T06:55:20Z"},{"publication_status":"published","publication_identifier":{"issn":["0021-9606","1089-7690"]},"year":"2018","citation":{"bibtex":"@article{Boninsegna_Nüske_Clementi_2018, title={Sparse learning of stochastic dynamical equations}, DOI={<a href=\"https://doi.org/10.1063/1.5018409\">10.1063/1.5018409</a>}, number={241723}, journal={The Journal of Chemical Physics}, author={Boninsegna, Lorenzo and Nüske, Feliks and Clementi, Cecilia}, year={2018} }","short":"L. Boninsegna, F. Nüske, C. Clementi, The Journal of Chemical Physics (2018).","mla":"Boninsegna, Lorenzo, et al. “Sparse Learning of Stochastic Dynamical Equations.” <i>The Journal of Chemical Physics</i>, 241723, 2018, doi:<a href=\"https://doi.org/10.1063/1.5018409\">10.1063/1.5018409</a>.","apa":"Boninsegna, L., Nüske, F., &#38; Clementi, C. (2018). Sparse learning of stochastic dynamical equations. <i>The Journal of Chemical Physics</i>. <a href=\"https://doi.org/10.1063/1.5018409\">https://doi.org/10.1063/1.5018409</a>","ama":"Boninsegna L, Nüske F, Clementi C. Sparse learning of stochastic dynamical equations. <i>The Journal of Chemical Physics</i>. 2018. doi:<a href=\"https://doi.org/10.1063/1.5018409\">10.1063/1.5018409</a>","chicago":"Boninsegna, Lorenzo, Feliks Nüske, and Cecilia Clementi. “Sparse Learning of Stochastic Dynamical Equations.” <i>The Journal of Chemical Physics</i>, 2018. <a href=\"https://doi.org/10.1063/1.5018409\">https://doi.org/10.1063/1.5018409</a>.","ieee":"L. Boninsegna, F. Nüske, and C. Clementi, “Sparse learning of stochastic dynamical equations,” <i>The Journal of Chemical Physics</i>, 2018."},"date_updated":"2022-01-06T06:55:20Z","date_created":"2021-04-30T16:59:39Z","author":[{"full_name":"Boninsegna, Lorenzo","last_name":"Boninsegna","first_name":"Lorenzo"},{"full_name":"Nüske, Feliks","id":"81513","orcid":"0000-0003-2444-7889","last_name":"Nüske","first_name":"Feliks"},{"first_name":"Cecilia","last_name":"Clementi","full_name":"Clementi, Cecilia"}],"title":"Sparse learning of stochastic dynamical equations","doi":"10.1063/1.5018409","type":"journal_article","publication":"The Journal of Chemical Physics","status":"public","_id":"21942","user_id":"81513","department":[{"_id":"101"}],"article_number":"241723","extern":"1","language":[{"iso":"eng"}]},{"status":"public","publication":"The Journal of Chemical Physics","type":"journal_article","article_number":"244119","language":[{"iso":"eng"}],"extern":"1","_id":"21943","department":[{"_id":"101"}],"user_id":"81513","year":"2018","citation":{"apa":"Hruska, E., Abella, J. R., Nüske, F., Kavraki, L. E., &#38; Clementi, C. (2018). Quantitative comparison of adaptive sampling methods for protein dynamics. <i>The Journal of Chemical Physics</i>. <a href=\"https://doi.org/10.1063/1.5053582\">https://doi.org/10.1063/1.5053582</a>","bibtex":"@article{Hruska_Abella_Nüske_Kavraki_Clementi_2018, title={Quantitative comparison of adaptive sampling methods for protein dynamics}, DOI={<a href=\"https://doi.org/10.1063/1.5053582\">10.1063/1.5053582</a>}, number={244119}, journal={The Journal of Chemical Physics}, author={Hruska, Eugen and Abella, Jayvee R. and Nüske, Feliks and Kavraki, Lydia E. and Clementi, Cecilia}, year={2018} }","mla":"Hruska, Eugen, et al. “Quantitative Comparison of Adaptive Sampling Methods for Protein Dynamics.” <i>The Journal of Chemical Physics</i>, 244119, 2018, doi:<a href=\"https://doi.org/10.1063/1.5053582\">10.1063/1.5053582</a>.","short":"E. Hruska, J.R. Abella, F. Nüske, L.E. Kavraki, C. Clementi, The Journal of Chemical Physics (2018).","ama":"Hruska E, Abella JR, Nüske F, Kavraki LE, Clementi C. Quantitative comparison of adaptive sampling methods for protein dynamics. <i>The Journal of Chemical Physics</i>. 2018. doi:<a href=\"https://doi.org/10.1063/1.5053582\">10.1063/1.5053582</a>","chicago":"Hruska, Eugen, Jayvee R. Abella, Feliks Nüske, Lydia E. Kavraki, and Cecilia Clementi. “Quantitative Comparison of Adaptive Sampling Methods for Protein Dynamics.” <i>The Journal of Chemical Physics</i>, 2018. <a href=\"https://doi.org/10.1063/1.5053582\">https://doi.org/10.1063/1.5053582</a>.","ieee":"E. Hruska, J. R. Abella, F. Nüske, L. E. Kavraki, and C. Clementi, “Quantitative comparison of adaptive sampling methods for protein dynamics,” <i>The Journal of Chemical Physics</i>, 2018."},"publication_identifier":{"issn":["0021-9606","1089-7690"]},"publication_status":"published","title":"Quantitative comparison of adaptive sampling methods for protein dynamics","doi":"10.1063/1.5053582","date_updated":"2022-01-06T06:55:20Z","date_created":"2021-04-30T17:00:24Z","author":[{"last_name":"Hruska","full_name":"Hruska, Eugen","first_name":"Eugen"},{"full_name":"Abella, Jayvee R.","last_name":"Abella","first_name":"Jayvee R."},{"id":"81513","full_name":"Nüske, Feliks","orcid":"0000-0003-2444-7889","last_name":"Nüske","first_name":"Feliks"},{"first_name":"Lydia E.","last_name":"Kavraki","full_name":"Kavraki, Lydia E."},{"full_name":"Clementi, Cecilia","last_name":"Clementi","first_name":"Cecilia"}]},{"department":[{"_id":"101"}],"user_id":"81513","_id":"21938","extern":"1","language":[{"iso":"eng"}],"article_number":"094104","publication":"The Journal of Chemical Physics","type":"journal_article","status":"public","author":[{"orcid":"0000-0003-2444-7889","last_name":"Nüske","full_name":"Nüske, Feliks","id":"81513","first_name":"Feliks"},{"first_name":"Hao","last_name":"Wu","full_name":"Wu, Hao"},{"first_name":"Jan-Hendrik","full_name":"Prinz, Jan-Hendrik","last_name":"Prinz"},{"first_name":"Christoph","full_name":"Wehmeyer, Christoph","last_name":"Wehmeyer"},{"first_name":"Cecilia","full_name":"Clementi, Cecilia","last_name":"Clementi"},{"first_name":"Frank","full_name":"Noé, Frank","last_name":"Noé"}],"date_created":"2021-04-30T16:55:31Z","date_updated":"2022-01-06T06:55:20Z","doi":"10.1063/1.4976518","title":"Markov state models from short non-equilibrium simulations—Analysis and correction of estimation bias","publication_identifier":{"issn":["0021-9606","1089-7690"]},"publication_status":"published","citation":{"ama":"Nüske F, Wu H, Prinz J-H, Wehmeyer C, Clementi C, Noé F. Markov state models from short non-equilibrium simulations—Analysis and correction of estimation bias. <i>The Journal of Chemical Physics</i>. 2017. doi:<a href=\"https://doi.org/10.1063/1.4976518\">10.1063/1.4976518</a>","chicago":"Nüske, Feliks, Hao Wu, Jan-Hendrik Prinz, Christoph Wehmeyer, Cecilia Clementi, and Frank Noé. “Markov State Models from Short Non-Equilibrium Simulations—Analysis and Correction of Estimation Bias.” <i>The Journal of Chemical Physics</i>, 2017. <a href=\"https://doi.org/10.1063/1.4976518\">https://doi.org/10.1063/1.4976518</a>.","ieee":"F. Nüske, H. Wu, J.-H. Prinz, C. Wehmeyer, C. Clementi, and F. Noé, “Markov state models from short non-equilibrium simulations—Analysis and correction of estimation bias,” <i>The Journal of Chemical Physics</i>, 2017.","bibtex":"@article{Nüske_Wu_Prinz_Wehmeyer_Clementi_Noé_2017, title={Markov state models from short non-equilibrium simulations—Analysis and correction of estimation bias}, DOI={<a href=\"https://doi.org/10.1063/1.4976518\">10.1063/1.4976518</a>}, number={094104}, journal={The Journal of Chemical Physics}, author={Nüske, Feliks and Wu, Hao and Prinz, Jan-Hendrik and Wehmeyer, Christoph and Clementi, Cecilia and Noé, Frank}, year={2017} }","short":"F. Nüske, H. Wu, J.-H. Prinz, C. Wehmeyer, C. Clementi, F. Noé, The Journal of Chemical Physics (2017).","mla":"Nüske, Feliks, et al. “Markov State Models from Short Non-Equilibrium Simulations—Analysis and Correction of Estimation Bias.” <i>The Journal of Chemical Physics</i>, 094104, 2017, doi:<a href=\"https://doi.org/10.1063/1.4976518\">10.1063/1.4976518</a>.","apa":"Nüske, F., Wu, H., Prinz, J.-H., Wehmeyer, C., Clementi, C., &#38; Noé, F. (2017). 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