8015
2020
2021
eng
758
774
2
19
article
SIAM
0
2021-04-27
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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.
Multiscale Modeling and Simulation
10.1137/20M1333006
yes
2021-02-09
Renata Sechi
Alexander Sikorski
Alexander Sikorski
Marcus Weber
Numerical Mathematics
Weber, Marcus
SFB1114-A5
Sikorski, Alexander
Sechi, Renata
Modeling and Simulation of Complex Processes