---
_id: '30125'
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.
author:
- first_name: Manuel
  full_name: Schaller, Manuel
  last_name: Schaller
- first_name: Karl
  full_name: Worthmann, Karl
  last_name: Worthmann
- first_name: Friedrich
  full_name: Philipp, Friedrich
  last_name: Philipp
- first_name: Sebastian
  full_name: Peitz, Sebastian
  id: '47427'
  last_name: Peitz
  orcid: 0000-0002-3389-793X
- first_name: Feliks
  full_name: Nüske, Feliks
  id: '81513'
  last_name: Nüske
  orcid: 0000-0003-2444-7889
citation:
  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>'
  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>
  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>.'
  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.'
conference:
  name: 12th IFAC Symposium on Nonlinear Control Systems (NOLCOS)
date_created: 2022-02-25T17:14:58Z
date_updated: 2023-03-17T15:55:33Z
department:
- _id: '655'
doi: 10.1016/j.ifacol.2023.02.029
external_id:
  arxiv:
  - '2202.09084'
intvolume: '        56'
issue: '1'
language:
- iso: eng
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
oa: '1'
page: 169-174
publication: IFAC-PapersOnLine
publication_status: published
status: public
title: Towards reliable data-based optimal and predictive control using extended DMD
type: conference
user_id: '47427'
volume: 56
year: '2023'
...
---
_id: '23428'
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."
article_number: '14'
author:
- 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: 0000-0002-3389-793X
- first_name: Friedrich
  full_name: Philipp, Friedrich
  last_name: Philipp
- first_name: Manuel
  full_name: Schaller, Manuel
  last_name: Schaller
- first_name: Karl
  full_name: Worthmann, Karl
  last_name: Worthmann
citation:
  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>
  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} }'
  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>.'
  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>.
  short: F. Nüske, S. Peitz, F. Philipp, M. Schaller, K. Worthmann, Journal of Nonlinear
    Science 33 (2023).
date_created: 2021-08-17T12:25:09Z
date_updated: 2023-08-24T07:50:12Z
department:
- _id: '101'
- _id: '655'
doi: 10.1007/s00332-022-09862-1
intvolume: '        33'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://link.springer.com/content/pdf/10.1007/s00332-022-09862-1.pdf
oa: '1'
publication: Journal of Nonlinear Science
publication_status: published
status: public
title: Finite-data error bounds for Koopman-based prediction and control
type: journal_article
user_id: '47427'
volume: 33
year: '2023'
...
---
_id: '29673'
abstract:
- lang: eng
  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.
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: 0000-0002-3389-793X
citation:
  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} }'
  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>.'
  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>.'
  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.'
date_created: 2022-01-31T09:49:40Z
date_updated: 2022-07-18T14:26:41Z
department:
- _id: '655'
- _id: '101'
doi: 10.1088/1751-8121/ac7d22
external_id:
  arxiv:
  - '2201.12062'
intvolume: '        55'
issue: '31'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://iopscience.iop.org/article/10.1088/1751-8121/ac7d22/pdf
oa: '1'
page: '314002'
publication: 'Journal of Physics A: Mathematical and Theoretical'
publication_status: published
publisher: IOP Publishing Ltd.
status: public
title: Koopman analysis of quantum systems
type: journal_article
user_id: '47427'
volume: 55
year: '2022'
...
---
_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: '24170'
article_number: '045016'
author:
- first_name: Stefan
  full_name: Klus, Stefan
  last_name: Klus
- first_name: Patrick
  full_name: Gelß, Patrick
  last_name: Gelß
- first_name: Feliks
  full_name: Nüske, Feliks
  id: '81513'
  last_name: Nüske
  orcid: 0000-0003-2444-7889
- first_name: Frank
  full_name: Noé, Frank
  last_name: Noé
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>'
  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} }'
  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>.'
  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>.'
  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>.'
  short: 'S. Klus, P. Gelß, F. Nüske, F. Noé, Machine Learning: Science and Technology
    (2021).'
date_created: 2021-09-12T08:52:57Z
date_updated: 2022-01-06T06:56:08Z
department:
- _id: '101'
doi: 10.1088/2632-2153/ac14ad
language:
- iso: eng
publication: 'Machine Learning: Science and Technology'
publication_identifier:
  issn:
  - 2632-2153
publication_status: published
status: public
title: Symmetric and antisymmetric kernels for machine learning problems in quantum
  physics and chemistry
type: journal_article
user_id: '81513'
year: '2021'
...
---
_id: '21820'
abstract:
- lang: eng
  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>
article_number: '134'
author:
- first_name: Feliks
  full_name: Nüske, Feliks
  id: '81513'
  last_name: Nüske
  orcid: 0000-0003-2444-7889
- first_name: Péter
  full_name: Koltai, Péter
  last_name: Koltai
- first_name: Lorenzo
  full_name: Boninsegna, Lorenzo
  last_name: Boninsegna
- first_name: Cecilia
  full_name: Clementi, Cecilia
  last_name: Clementi
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>
  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>
  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} }'
  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.
  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>.
  short: F. Nüske, P. Koltai, L. Boninsegna, C. Clementi, Entropy (2021).
date_created: 2021-04-28T18:07:56Z
date_updated: 2022-01-06T06:55:16Z
department:
- _id: '101'
doi: 10.3390/e23020134
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://www.mdpi.com/1099-4300/23/2/134
oa: '1'
publication: Entropy
publication_identifier:
  issn:
  - 1099-4300
publication_status: published
status: public
title: Spectral Properties of Effective Dynamics from Conditional Expectations
type: journal_article
user_id: '81513'
year: '2021'
...
---
_id: '21819'
abstract:
- lang: eng
  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>
article_number: '722'
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: Boumediene
  full_name: Hamzi, Boumediene
  last_name: Hamzi
citation:
  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>
  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>
  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} }'
  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.
  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>.
  short: S. Klus, F. Nüske, B. Hamzi, Entropy (2020).
date_created: 2021-04-28T18:06:35Z
date_updated: 2022-01-06T06:55:16Z
department:
- _id: '101'
doi: 10.3390/e22070722
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://www.mdpi.com/1099-4300/22/7/722
oa: '1'
publication: Entropy
publication_identifier:
  issn:
  - 1099-4300
publication_status: published
status: public
title: Kernel-Based Approximation of the Koopman Generator and Schrödinger Operator
type: journal_article
user_id: '81513'
year: '2020'
...
---
_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: '21944'
article_number: '044116'
author:
- first_name: Feliks
  full_name: Nüske, Feliks
  id: '81513'
  last_name: Nüske
  orcid: 0000-0003-2444-7889
- first_name: Lorenzo
  full_name: Boninsegna, Lorenzo
  last_name: Boninsegna
- first_name: Cecilia
  full_name: Clementi, Cecilia
  last_name: Clementi
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>
  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>
  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} }'
  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.
  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>.
  short: F. Nüske, L. Boninsegna, C. Clementi, The Journal of Chemical Physics (2019).
date_created: 2021-04-30T17:01:13Z
date_updated: 2022-01-06T06:55:20Z
department:
- _id: '101'
doi: 10.1063/1.5100131
extern: '1'
language:
- iso: eng
publication: The Journal of Chemical Physics
publication_identifier:
  issn:
  - 0021-9606
  - 1089-7690
publication_status: published
status: public
title: Coarse-graining molecular systems by spectral matching
type: journal_article
user_id: '81513'
year: '2019'
...
---
_id: '21940'
author:
- first_name: Florian
  full_name: Litzinger, Florian
  last_name: Litzinger
- first_name: Lorenzo
  full_name: Boninsegna, Lorenzo
  last_name: Boninsegna
- first_name: Hao
  full_name: Wu, Hao
  last_name: Wu
- first_name: Feliks
  full_name: Nüske, Feliks
  id: '81513'
  last_name: Nüske
  orcid: 0000-0003-2444-7889
- first_name: Raajen
  full_name: Patel, Raajen
  last_name: Patel
- first_name: Richard
  full_name: Baraniuk, Richard
  last_name: Baraniuk
- first_name: Frank
  full_name: Noé, Frank
  last_name: Noé
- first_name: Cecilia
  full_name: Clementi, Cecilia
  last_name: Clementi
citation:
  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>
  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>
  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}
    }'
  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>.
  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.
  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.
date_created: 2021-04-30T16:58:07Z
date_updated: 2022-01-06T06:55:20Z
department:
- _id: '101'
doi: 10.1021/acs.jctc.8b00089
extern: '1'
language:
- iso: eng
page: 2771-2783
publication: Journal of Chemical Theory and Computation
publication_identifier:
  issn:
  - 1549-9618
  - 1549-9626
publication_status: published
status: public
title: Rapid Calculation of Molecular Kinetics Using Compressed Sensing
type: journal_article
user_id: '81513'
year: '2018'
...
---
_id: '21941'
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: Péter
  full_name: Koltai, Péter
  last_name: Koltai
- first_name: Hao
  full_name: Wu, Hao
  last_name: Wu
- first_name: Ioannis
  full_name: Kevrekidis, Ioannis
  last_name: Kevrekidis
- first_name: Christof
  full_name: Schütte, Christof
  last_name: Schütte
- first_name: Frank
  full_name: Noé, Frank
  last_name: Noé
citation:
  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>
  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>
  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} }'
  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>.
  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.
  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>.
  short: S. Klus, F. Nüske, P. Koltai, H. Wu, I. Kevrekidis, C. Schütte, F. Noé, Journal
    of Nonlinear Science (2018) 985–1010.
date_created: 2021-04-30T16:59:03Z
date_updated: 2022-01-06T06:55:20Z
department:
- _id: '101'
doi: 10.1007/s00332-017-9437-7
extern: '1'
language:
- iso: eng
page: 985-1010
publication: Journal of Nonlinear Science
publication_identifier:
  issn:
  - 0938-8974
  - 1432-1467
publication_status: published
status: public
title: Data-Driven Model Reduction and Transfer Operator Approximation
type: journal_article
user_id: '81513'
year: '2018'
...
---
_id: '21942'
article_number: '241723'
author:
- first_name: Lorenzo
  full_name: Boninsegna, Lorenzo
  last_name: Boninsegna
- first_name: Feliks
  full_name: Nüske, Feliks
  id: '81513'
  last_name: Nüske
  orcid: 0000-0003-2444-7889
- first_name: Cecilia
  full_name: Clementi, Cecilia
  last_name: Clementi
citation:
  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>
  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>
  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} }'
  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.
  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>.
  short: L. Boninsegna, F. Nüske, C. Clementi, The Journal of Chemical Physics (2018).
date_created: 2021-04-30T16:59:39Z
date_updated: 2022-01-06T06:55:20Z
department:
- _id: '101'
doi: 10.1063/1.5018409
extern: '1'
language:
- iso: eng
publication: The Journal of Chemical Physics
publication_identifier:
  issn:
  - 0021-9606
  - 1089-7690
publication_status: published
status: public
title: Sparse learning of stochastic dynamical equations
type: journal_article
user_id: '81513'
year: '2018'
...
---
_id: '21943'
article_number: '244119'
author:
- first_name: Eugen
  full_name: Hruska, Eugen
  last_name: Hruska
- first_name: Jayvee R.
  full_name: Abella, Jayvee R.
  last_name: Abella
- first_name: Feliks
  full_name: Nüske, Feliks
  id: '81513'
  last_name: Nüske
  orcid: 0000-0003-2444-7889
- first_name: Lydia E.
  full_name: Kavraki, Lydia E.
  last_name: Kavraki
- first_name: Cecilia
  full_name: Clementi, Cecilia
  last_name: Clementi
citation:
  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>
  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} }'
  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.
  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).
date_created: 2021-04-30T17:00:24Z
date_updated: 2022-01-06T06:55:20Z
department:
- _id: '101'
doi: 10.1063/1.5053582
extern: '1'
language:
- iso: eng
publication: The Journal of Chemical Physics
publication_identifier:
  issn:
  - 0021-9606
  - 1089-7690
publication_status: published
status: public
title: Quantitative comparison of adaptive sampling methods for protein dynamics
type: journal_article
user_id: '81513'
year: '2018'
...
---
_id: '21938'
article_number: '094104'
author:
- first_name: Feliks
  full_name: Nüske, Feliks
  id: '81513'
  last_name: Nüske
  orcid: 0000-0003-2444-7889
- first_name: Hao
  full_name: Wu, Hao
  last_name: Wu
- 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
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>
  apa: Nüske, F., Wu, H., Prinz, J.-H., Wehmeyer, C., Clementi, C., &#38; Noé, F.
    (2017). Markov state models from short non-equilibrium simulations—Analysis and
    correction of estimation bias. <i>The Journal of Chemical Physics</i>. <a href="https://doi.org/10.1063/1.4976518">https://doi.org/10.1063/1.4976518</a>
  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} }'
  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.
  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>.
  short: F. Nüske, H. Wu, J.-H. Prinz, C. Wehmeyer, C. Clementi, F. Noé, The Journal
    of Chemical Physics (2017).
date_created: 2021-04-30T16:55:31Z
date_updated: 2022-01-06T06:55:20Z
department:
- _id: '101'
doi: 10.1063/1.4976518
extern: '1'
language:
- iso: eng
publication: The Journal of Chemical Physics
publication_identifier:
  issn:
  - 0021-9606
  - 1089-7690
publication_status: published
status: public
title: Markov state models from short non-equilibrium simulations—Analysis and correction
  of estimation bias
type: journal_article
user_id: '81513'
year: '2017'
...
---
_id: '21939'
article_number: '154104'
author:
- first_name: Hao
  full_name: Wu, Hao
  last_name: Wu
- first_name: Feliks
  full_name: Nüske, Feliks
  id: '81513'
  last_name: Nüske
  orcid: 0000-0003-2444-7889
- first_name: Fabian
  full_name: Paul, Fabian
  last_name: Paul
- first_name: Stefan
  full_name: Klus, Stefan
  last_name: Klus
- first_name: Péter
  full_name: Koltai, Péter
  last_name: Koltai
- first_name: Frank
  full_name: Noé, Frank
  last_name: Noé
citation:
  ama: 'Wu H, Nüske F, Paul F, Klus S, Koltai P, Noé F. Variational Koopman models:
    Slow collective variables and molecular kinetics from short off-equilibrium simulations.
    <i>The Journal of Chemical Physics</i>. 2017. doi:<a href="https://doi.org/10.1063/1.4979344">10.1063/1.4979344</a>'
  apa: 'Wu, H., Nüske, F., Paul, F., Klus, S., Koltai, P., &#38; Noé, F. (2017). Variational
    Koopman models: Slow collective variables and molecular kinetics from short off-equilibrium
    simulations. <i>The Journal of Chemical Physics</i>. <a href="https://doi.org/10.1063/1.4979344">https://doi.org/10.1063/1.4979344</a>'
  bibtex: '@article{Wu_Nüske_Paul_Klus_Koltai_Noé_2017, title={Variational Koopman
    models: Slow collective variables and molecular kinetics from short off-equilibrium
    simulations}, DOI={<a href="https://doi.org/10.1063/1.4979344">10.1063/1.4979344</a>},
    number={154104}, journal={The Journal of Chemical Physics}, author={Wu, Hao and
    Nüske, Feliks and Paul, Fabian and Klus, Stefan and Koltai, Péter and Noé, Frank},
    year={2017} }'
  chicago: 'Wu, Hao, Feliks Nüske, Fabian Paul, Stefan Klus, Péter Koltai, and Frank
    Noé. “Variational Koopman Models: Slow Collective Variables and Molecular Kinetics
    from Short off-Equilibrium Simulations.” <i>The Journal of Chemical Physics</i>,
    2017. <a href="https://doi.org/10.1063/1.4979344">https://doi.org/10.1063/1.4979344</a>.'
  ieee: 'H. Wu, F. Nüske, F. Paul, S. Klus, P. Koltai, and F. Noé, “Variational Koopman
    models: Slow collective variables and molecular kinetics from short off-equilibrium
    simulations,” <i>The Journal of Chemical Physics</i>, 2017.'
  mla: 'Wu, Hao, et al. “Variational Koopman Models: Slow Collective Variables and
    Molecular Kinetics from Short off-Equilibrium Simulations.” <i>The Journal of
    Chemical Physics</i>, 154104, 2017, doi:<a href="https://doi.org/10.1063/1.4979344">10.1063/1.4979344</a>.'
  short: H. Wu, F. Nüske, F. Paul, S. Klus, P. Koltai, F. Noé, The Journal of Chemical
    Physics (2017).
date_created: 2021-04-30T16:57:21Z
date_updated: 2022-01-06T06:55:20Z
department:
- _id: '101'
doi: 10.1063/1.4979344
extern: '1'
language:
- iso: eng
publication: The Journal of Chemical Physics
publication_identifier:
  issn:
  - 0021-9606
  - 1089-7690
publication_status: published
status: public
title: 'Variational Koopman models: Slow collective variables and molecular kinetics
  from short off-equilibrium simulations'
type: journal_article
user_id: '81513'
year: '2017'
...
---
_id: '21937'
article_number: '054105'
author:
- first_name: Feliks
  full_name: Nüske, Feliks
  id: '81513'
  last_name: Nüske
  orcid: 0000-0003-2444-7889
- first_name: Reinhold
  full_name: Schneider, Reinhold
  last_name: Schneider
- first_name: Francesca
  full_name: Vitalini, Francesca
  last_name: Vitalini
- first_name: Frank
  full_name: Noé, Frank
  last_name: Noé
citation:
  ama: Nüske F, Schneider R, Vitalini F, Noé F. Variational tensor approach for approximating
    the rare-event kinetics of macromolecular systems. <i>The Journal of Chemical
    Physics</i>. 2016. doi:<a href="https://doi.org/10.1063/1.4940774">10.1063/1.4940774</a>
  apa: Nüske, F., Schneider, R., Vitalini, F., &#38; Noé, F. (2016). Variational tensor
    approach for approximating the rare-event kinetics of macromolecular systems.
    <i>The Journal of Chemical Physics</i>. <a href="https://doi.org/10.1063/1.4940774">https://doi.org/10.1063/1.4940774</a>
  bibtex: '@article{Nüske_Schneider_Vitalini_Noé_2016, title={Variational tensor approach
    for approximating the rare-event kinetics of macromolecular systems}, DOI={<a
    href="https://doi.org/10.1063/1.4940774">10.1063/1.4940774</a>}, number={054105},
    journal={The Journal of Chemical Physics}, author={Nüske, Feliks and Schneider,
    Reinhold and Vitalini, Francesca and Noé, Frank}, year={2016} }'
  chicago: Nüske, Feliks, Reinhold Schneider, Francesca Vitalini, and Frank Noé. “Variational
    Tensor Approach for Approximating the Rare-Event Kinetics of Macromolecular Systems.”
    <i>The Journal of Chemical Physics</i>, 2016. <a href="https://doi.org/10.1063/1.4940774">https://doi.org/10.1063/1.4940774</a>.
  ieee: F. Nüske, R. Schneider, F. Vitalini, and F. Noé, “Variational tensor approach
    for approximating the rare-event kinetics of macromolecular systems,” <i>The Journal
    of Chemical Physics</i>, 2016.
  mla: Nüske, Feliks, et al. “Variational Tensor Approach for Approximating the Rare-Event
    Kinetics of Macromolecular Systems.” <i>The Journal of Chemical Physics</i>, 054105,
    2016, doi:<a href="https://doi.org/10.1063/1.4940774">10.1063/1.4940774</a>.
  short: F. Nüske, R. Schneider, F. Vitalini, F. Noé, The Journal of Chemical Physics
    (2016).
date_created: 2021-04-30T16:54:43Z
date_updated: 2022-01-06T06:55:20Z
department:
- _id: '101'
doi: 10.1063/1.4940774
extern: '1'
language:
- iso: eng
publication: The Journal of Chemical Physics
publication_identifier:
  issn:
  - 0021-9606
  - 1089-7690
publication_status: published
status: public
title: Variational tensor approach for approximating the rare-event kinetics of macromolecular
  systems
type: journal_article
user_id: '81513'
year: '2016'
...
---
_id: '21936'
author:
- first_name: Feliks
  full_name: Nüske, Feliks
  id: '81513'
  last_name: Nüske
  orcid: 0000-0003-2444-7889
- first_name: Bettina G.
  full_name: Keller, Bettina G.
  last_name: Keller
- first_name: Guillermo
  full_name: Pérez-Hernández, Guillermo
  last_name: Pérez-Hernández
- first_name: Antonia S. J. S.
  full_name: Mey, Antonia S. J. S.
  last_name: Mey
- first_name: Frank
  full_name: Noé, Frank
  last_name: Noé
citation:
  ama: Nüske F, Keller BG, Pérez-Hernández G, Mey ASJS, Noé F. Variational Approach
    to Molecular Kinetics. <i>Journal of Chemical Theory and Computation</i>. 2014:1739-1752.
    doi:<a href="https://doi.org/10.1021/ct4009156">10.1021/ct4009156</a>
  apa: Nüske, F., Keller, B. G., Pérez-Hernández, G., Mey, A. S. J. S., &#38; Noé,
    F. (2014). Variational Approach to Molecular Kinetics. <i>Journal of Chemical
    Theory and Computation</i>, 1739–1752. <a href="https://doi.org/10.1021/ct4009156">https://doi.org/10.1021/ct4009156</a>
  bibtex: '@article{Nüske_Keller_Pérez-Hernández_Mey_Noé_2014, title={Variational
    Approach to Molecular Kinetics}, DOI={<a href="https://doi.org/10.1021/ct4009156">10.1021/ct4009156</a>},
    journal={Journal of Chemical Theory and Computation}, author={Nüske, Feliks and
    Keller, Bettina G. and Pérez-Hernández, Guillermo and Mey, Antonia S. J. S. and
    Noé, Frank}, year={2014}, pages={1739–1752} }'
  chicago: Nüske, Feliks, Bettina G. Keller, Guillermo Pérez-Hernández, Antonia S.
    J. S. Mey, and Frank Noé. “Variational Approach to Molecular Kinetics.” <i>Journal
    of Chemical Theory and Computation</i>, 2014, 1739–52. <a href="https://doi.org/10.1021/ct4009156">https://doi.org/10.1021/ct4009156</a>.
  ieee: F. Nüske, B. G. Keller, G. Pérez-Hernández, A. S. J. S. Mey, and F. Noé, “Variational
    Approach to Molecular Kinetics,” <i>Journal of Chemical Theory and Computation</i>,
    pp. 1739–1752, 2014.
  mla: Nüske, Feliks, et al. “Variational Approach to Molecular Kinetics.” <i>Journal
    of Chemical Theory and Computation</i>, 2014, pp. 1739–52, doi:<a href="https://doi.org/10.1021/ct4009156">10.1021/ct4009156</a>.
  short: F. Nüske, B.G. Keller, G. Pérez-Hernández, A.S.J.S. Mey, F. Noé, Journal
    of Chemical Theory and Computation (2014) 1739–1752.
date_created: 2021-04-30T16:53:52Z
date_updated: 2022-01-06T06:55:20Z
department:
- _id: '101'
doi: 10.1021/ct4009156
extern: '1'
language:
- iso: eng
page: 1739-1752
publication: Journal of Chemical Theory and Computation
publication_identifier:
  issn:
  - 1549-9618
  - 1549-9626
publication_status: published
status: public
title: Variational Approach to Molecular Kinetics
type: journal_article
user_id: '81513'
year: '2014'
...
---
_id: '21935'
author:
- first_name: Frank
  full_name: Noé, Frank
  last_name: Noé
- first_name: Feliks
  full_name: Nüske, Feliks
  id: '81513'
  last_name: Nüske
  orcid: 0000-0003-2444-7889
citation:
  ama: Noé F, Nüske F. A Variational Approach to Modeling Slow Processes in Stochastic
    Dynamical Systems. <i>Multiscale Modeling &#38; Simulation</i>. 2013:635-655.
    doi:<a href="https://doi.org/10.1137/110858616">10.1137/110858616</a>
  apa: Noé, F., &#38; Nüske, F. (2013). A Variational Approach to Modeling Slow Processes
    in Stochastic Dynamical Systems. <i>Multiscale Modeling &#38; Simulation</i>,
    635–655. <a href="https://doi.org/10.1137/110858616">https://doi.org/10.1137/110858616</a>
  bibtex: '@article{Noé_Nüske_2013, title={A Variational Approach to Modeling Slow
    Processes in Stochastic Dynamical Systems}, DOI={<a href="https://doi.org/10.1137/110858616">10.1137/110858616</a>},
    journal={Multiscale Modeling &#38; Simulation}, author={Noé, Frank and Nüske,
    Feliks}, year={2013}, pages={635–655} }'
  chicago: Noé, Frank, and Feliks Nüske. “A Variational Approach to Modeling Slow
    Processes in Stochastic Dynamical Systems.” <i>Multiscale Modeling &#38; Simulation</i>,
    2013, 635–55. <a href="https://doi.org/10.1137/110858616">https://doi.org/10.1137/110858616</a>.
  ieee: F. Noé and F. Nüske, “A Variational Approach to Modeling Slow Processes in
    Stochastic Dynamical Systems,” <i>Multiscale Modeling &#38; Simulation</i>, pp.
    635–655, 2013.
  mla: Noé, Frank, and Feliks Nüske. “A Variational Approach to Modeling Slow Processes
    in Stochastic Dynamical Systems.” <i>Multiscale Modeling &#38; Simulation</i>,
    2013, pp. 635–55, doi:<a href="https://doi.org/10.1137/110858616">10.1137/110858616</a>.
  short: F. Noé, F. Nüske, Multiscale Modeling &#38; Simulation (2013) 635–655.
date_created: 2021-04-30T16:51:37Z
date_updated: 2022-01-06T06:55:20Z
department:
- _id: '101'
doi: 10.1137/110858616
extern: '1'
language:
- iso: eng
page: 635-655
publication: Multiscale Modeling & Simulation
publication_identifier:
  issn:
  - 1540-3459
  - 1540-3467
publication_status: published
status: public
title: A Variational Approach to Modeling Slow Processes in Stochastic Dynamical Systems
type: journal_article
user_id: '81513'
year: '2013'
...