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.
Author: | Renata Sechi, Alexander SikorskiORCiD, Marcus Weber |
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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 |