Repository: Freie Universität Berlin, Math Department

Kernel-Based Approximation of the Koopman Generator and Schrödinger Operator

Klus, Stefan and Nüske, Felix and Hamzi, Boumediene (2020) Kernel-Based Approximation of the Koopman Generator and Schrödinger Operator. entropy, 22 .

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Abstract 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.

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics
ID Code:2739
Deposited By: Monika Drueck
Deposited On:15 Feb 2022 17:57
Last Modified:15 Feb 2022 17:57

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