Entropic transfer operators

TL;DR

This paper introduces a novel entropic regularization method for transfer and Koopman operators in dynamical systems, enabling computationally feasible approximations with proven spectral convergence and practical applications including biomolecular data analysis.

Contribution

It presents a new entropic regularization approach for transfer operators, with theoretical convergence guarantees and demonstrated effectiveness in numerical experiments.

Findings

Spectral convergence of discretized operators to regularized originals

Analysis of peripheral spectrum for rotation maps on the n-torus

Successful application to biomolecular trajectory data

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 analysed 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.