Learning Koopman eigenfunctions of stochastic diffusions with optimal importance sampling and ISOKANN
Abstract
For stochastic diffusion processes the dominant eigenfunctions of the corresponding Koopman operator contain important information about the slow-scale dynamics, that is, about the location and frequency of rare events. In this article, we reformulate the eigenproblem in terms of -functions in the ISOKANN framework and discuss how optimal control and importance sampling allows for zero variance sampling of these functions. We provide a new formulation of the ISOKANN algorithm allowing for a proof of convergence and incorporate the optimal control result to obtain an adaptive iterative algorithm alternating between importance sampling and -function approximation. We demonstrate the usage of our proposed method in experiments increasing the approximation accuracy by several orders of magnitude.
Cite
@article{arxiv.2301.00065,
title = {Learning Koopman eigenfunctions of stochastic diffusions with optimal importance sampling and ISOKANN},
author = {Alexander Sikorski and Enric Ribera Borrell and Marcus Weber},
journal= {arXiv preprint arXiv:2301.00065},
year = {2024}
}