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.

Full text not available from this repository.

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 |
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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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