Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Kernel-based approximation of the Koopman generator and Schr\"odinger
  operator   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
Schr\"odinger 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 Schr\"odinger 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.

12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess