Kernel-Based Approximation of the Koopman Generator and Schrödinger Operator

S. Klus, F. Nüske, B. Hamzi, Entropy (2020).

Journal Article | Published | English
Author
Klus, Stefan; Nüske, FeliksLibreCat ; Hamzi, Boumediene
Abstract
<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>
Publishing Year
Journal Title
Entropy
Article Number
722
ISSN
LibreCat-ID

Cite this

Klus S, Nüske F, Hamzi B. Kernel-Based Approximation of the Koopman Generator and Schrödinger Operator. Entropy. 2020. doi:10.3390/e22070722
Klus, S., Nüske, F., & Hamzi, B. (2020). Kernel-Based Approximation of the Koopman Generator and Schrödinger Operator. Entropy. https://doi.org/10.3390/e22070722
@article{Klus_Nüske_Hamzi_2020, title={Kernel-Based Approximation of the Koopman Generator and Schrödinger Operator}, DOI={10.3390/e22070722}, number={722}, journal={Entropy}, author={Klus, Stefan and Nüske, Feliks and Hamzi, Boumediene}, year={2020} }
Klus, Stefan, Feliks Nüske, and Boumediene Hamzi. “Kernel-Based Approximation of the Koopman Generator and Schrödinger Operator.” Entropy, 2020. https://doi.org/10.3390/e22070722.
S. Klus, F. Nüske, and B. Hamzi, “Kernel-Based Approximation of the Koopman Generator and Schrödinger Operator,” Entropy, 2020.
Klus, Stefan, et al. “Kernel-Based Approximation of the Koopman Generator and Schrödinger Operator.” Entropy, 722, 2020, doi:10.3390/e22070722.
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