TY - JOUR A1 - Sechi, Renata A1 - Sikorski, Alexander A1 - Weber, Marcus T1 - Estimation of the Koopman Generator by Newton's Extrapolation T2 - Multiscale Modeling and Simulation N2 - 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. Y1 - 2021 UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/8015 VL - 19 IS - 2 SP - 758 EP - 774 PB - SIAM ER -