Repository: Freie Universit├Ąt Berlin, Math Department

Learning Koopman eigenfunctions of stochastic diffusions with optimal importance sampling and ISOKANN

Sikorski, Alexander and Ribera Borrell, Enric and Weber, Marcus (2024) Learning Koopman eigenfunctions of stochastic diffusions with optimal importance sampling and ISOKANN. Journal of Mathematical Physics, 65 (1).

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Official URL: https://doi.org/10.1063/5.0140764

Abstract

The dominant eigenfunctions of the Koopman operator characterize the metastabilities and slow-timescale dynamics of stochastic diffusion processes. In the context of molecular dynamics and Markov state modeling, they allow for a description of the location and frequencies of rare transitions, which are hard to obtain by direct simulation alone. In this article, we reformulate the eigenproblem in terms of the ISOKANN framework, an iterative algorithm that learns the eigenfunctions by alternating between short burst simulations and a mixture of machine learning and classical numerics, which naturally leads to a proof of convergence. We furthermore show how the intermediate iterates can be used to reduce the sampling variance by importance sampling and optimal control (enhanced sampling), as well as to select locations for further training (adaptive sampling). We demonstrate the usage of our proposed method in experiments, increasing the approximation accuracy by several orders of magnitude.

Item Type:Article
Subjects:Mathematical and Computer Sciences
Mathematical and Computer Sciences > Mathematics
Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics
ID Code:3048
Deposited By: Jana Jerosch
Deposited On:18 Jan 2024 12:43
Last Modified:18 Jan 2024 12:43

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