Estimation of the Koopman Generator by Newton's Extrapolation

  • 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.

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Metadaten
Author:Renata Sechi, Alexander SikorskiORCiD, Marcus Weber
Document Type:Article
Parent Title (English):Multiscale Modeling and Simulation
Volume:19
Issue:2
First Page:758
Last Page:774
Publisher:SIAM
Year of first publication:2021
DOI:https://doi.org/10.1137/20M1333006