6267
2018
eng
985
1010
3
28
article
0
2018-01-03
--
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Data-driven model reduction and transfer operator approximation
Journal of Nonlinear Science
https://link.springer.com/article/10.1007/s00332-017-9437-7
10.1007/s00332-017-9437-7
yes
Stefan Klus
Erlinda Koernig
Feliks Nüske
Peter Koltai
Hao Wu
Ioannis Kevrekidis
Christof Schütte
Frank Noé
Numerical Mathematics
Schütte, Christof
MODAL-MedLab
SFB1114-A5
MODAL-Gesamt
8502
2022
eng
32
article
0
--
--
--
tgEDMD: Approximation of the Kolmogorov Operator in Tensor Train Format
Extracting information about dynamical systems from models learned off simulation data has become an increasingly important research topic in the natural and engineering sciences. Modeling the Koopman operator semigroup has played a central role in this context. As the approximation quality of any such model critically depends on the basis set, recent work has focused on deriving data-efficient representations of the Koopman operator in low-rank tensor formats, enabling the use of powerful model classes while avoiding over-fitting. On the other hand, detailed information about the system at hand can be extracted from models for the infinitesimal generator, also called Kolmogorov backward operator for stochastic differential equations. In this work, we present a data-driven method to efficiently approximate the generator using the tensor train (TT) format. The centerpiece of the method is a TT representation of the tensor of generator evaluations at all data sites. We analyze consistency and complexity of the method, present extensions to practically relevant settings, and demonstrate its applicability to benchmark numerical examples.
Journal of Nonlinear Science
10.1007/s00332-022-09801-0
publish
yes
Marvin Lücke
Marvin Lücke
Feliks Nüske
Modeling and Simulation of Complex Processes
Lücke, Marvin
MathPlusEF4-8
7589
2020
eng
406
article
0
2020-03-06
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Data-driven approximation of the Koopman generator: Model reduction, system identification, and control
Physica D: Nonlinear Phenomena
10.1016/j.physd.2020.132416
yes
epub ahead of print
Stefan Klus
Erlinda Körnig
Feliks Nüske
Sebastian Peitz
Jan-Hendrik Niemann
Cecilia Clementi
Christof Schütte
Numerical Mathematics
Schütte, Christof
MODAL-MedLab
MODAL-Gesamt
MathPlusAA1-1
Modeling and Simulation of Complex Processes