Repository: Freie Universit├Ąt Berlin, Math Department

Estimation of the Koopman Generator by Newton's Extrapolation

Sechi, Renata and Sikorski, Alexander and Weber, Marcus (2021) Estimation of the Koopman Generator by Newton's Extrapolation. Multiscale Modeling & Simulation, 19 (2). pp. 758-774.

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Official URL: https://doi.org/10.1137/20M1333006

Abstract

This article addresses the problem of estimating the Koopman generator of a Markov process. The direct computation of the infinitesimal generator is not easy because of the discretization of the state space, in particular because of the trade-off inherent in the choice of the best lag time to study the process. Short lag times implies a strong discretization of the state space and a consequent loss of Markovianity. Large lag times bypass events on fast timescales. We propose a method to approximate the generator with the computation of the Newton polynomial extrapolation. This technique is a multistep approach which uses as its input Koopman transfer operators evaluated for a series of lag times. Thus, the estimated infinitesimal generator combines information from different time resolutions and does not bias only fast- or slow-decaying dynamics. We show that the multi-scale Newton method can improve the estimation of the generator in comparison to the computation using finite difference or matrix logarithm methods. Read More: https://epubs.siam.org/doi/abs/10.1137/20M1333006?mobileUi=0

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics
ID Code:2733
Deposited By: Monika Drueck
Deposited On:15 Feb 2022 17:17
Last Modified:15 Feb 2022 17:17

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