---
_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'
...