id,collection,dc.contributor.author,dc.date.accessioned,dc.date.available,dc.date.issued,dc.description.abstract[en],dc.format.extent,dc.identifier.uri,dc.language,dc.rights.uri,dc.subject.ddc,dc.subject[en],dc.title,dc.type,dcterms.accessRights.openaire,dcterms.bibliographicCitation.articlenumber,dcterms.bibliographicCitation.doi,dcterms.bibliographicCitation.journaltitle,dcterms.bibliographicCitation.number,dcterms.bibliographicCitation.originalpublishername,dcterms.bibliographicCitation.url,dcterms.bibliographicCitation.volume,dcterms.isPartOf.eissn,refubium.affiliation,refubium.note.author "80ebb778-7244-4938-a88b-e17e0cc93468","fub188/16","Klus, Stefan||Nüske, Feliks||Hamzi, Boumediene","2020-10-29T15:21:07Z","2020-10-29T15:21:07Z","2020","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.","22 Seiten","https://refubium.fu-berlin.de/handle/fub188/28716||http://dx.doi.org/10.17169/refubium-28464","eng","https://creativecommons.org/licenses/by/4.0/","500 Naturwissenschaften und Mathematik::510 Mathematik::510 Mathematik","Koopman generator||Schrödinger operator||reproducing kernel Hilbert space","Kernel-Based Approximation of the Koopman Generator and Schrödinger Operator","Wissenschaftlicher Artikel","open access","722","10.3390/e22070722","Entropy","7","MDPI","https://doi.org/10.3390/e22070722","22","1099-4300","Mathematik und Informatik","Die Publikation wurde aus Open Access Publikationsgeldern der Freien Universität Berlin gefördert."