TY - JOUR
T1 - Data-Driven Model Reduction and Transfer Operator Approximation
AU - Klus, Stefan
AU - Nüske, Feliks
AU - Koltai, Péter
AU - Wu, Hao
AU - Kevrekidis, Ioannis
AU - Schütte, Christof
AU - Noé, Frank
N1 - Funding Information:
Acknowledgements This research has been partially funded by Deutsche Forschungsgemeinschaft (DFG) through grant CRC 1114 “Scaling Cascades in Complex Systems,” Project A04 “Efficient calculation of slow and stationary scales in molecular dynamics” and Project B03 “Multilevel coarse graining of multi-scale problems”, and by the Einstein Foundation Berlin (Einstein Center ECMath). Furthermore, we would like to thank the reviewers for their helpful comments and suggestions.
Publisher Copyright:
© 2017, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2018/6
Y1 - 2018/6
N2 - In this review paper, we will present different data-driven dimension reduction techniques for dynamical systems that are based on transfer operator theory as well as methods to approximate transfer operators and their eigenvalues, eigenfunctions, and eigenmodes. The goal is to point out similarities and differences between methods developed independently by the dynamical systems, fluid dynamics, and molecular dynamics communities such as time-lagged independent component analysis, dynamic mode decomposition, and their respective generalizations. As a result, extensions and best practices developed for one particular method can be carried over to other related methods.
AB - In this review paper, we will present different data-driven dimension reduction techniques for dynamical systems that are based on transfer operator theory as well as methods to approximate transfer operators and their eigenvalues, eigenfunctions, and eigenmodes. The goal is to point out similarities and differences between methods developed independently by the dynamical systems, fluid dynamics, and molecular dynamics communities such as time-lagged independent component analysis, dynamic mode decomposition, and their respective generalizations. As a result, extensions and best practices developed for one particular method can be carried over to other related methods.
KW - Data-driven methods
KW - Koopman operator
KW - Model reduction
KW - Perron-Frobenius operator
UR - http://www.scopus.com/inward/record.url?scp=85040047019&partnerID=8YFLogxK
U2 - 10.1007/s00332-017-9437-7
DO - 10.1007/s00332-017-9437-7
M3 - Article
AN - SCOPUS:85040047019
SN - 0938-8974
VL - 28
SP - 985
EP - 1010
JO - Journal of Nonlinear Science
JF - Journal of Nonlinear Science
IS - 3
ER -