Entropic transfer operators

Oliver Junge, Daniel Matthes, Bernhard Schmitzer

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We propose a new concept for the regularization and discretization of transfer and Koopman operators in dynamical systems. Our approach is based on the entropically regularized optimal transport between two probability measures. In particular, we use optimal transport plans in order to construct a finite-dimensional approximation of some transfer or Koopman operator which can be analyzed computationally. We prove that the spectrum of the discretized operator converges to the one of the regularized original operator, give a detailed analysis of the relation between the discretized and the original peripheral spectrum for a rotation map on the n-torus and provide code for three numerical experiments, including one based on the raw trajectory data of a small biomolecule from which its dominant conformations are recovered.

Original languageEnglish
Article number065004
JournalNonlinearity
Volume37
Issue number6
DOIs
StatePublished - 3 Jun 2024

Keywords

  • 37M25
  • entropic regularization
  • optimal transport
  • transfer operator

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