期刊
JOURNAL OF NONLINEAR SCIENCE
卷 28, 期 3, 页码 985-1010出版社
SPRINGER
DOI: 10.1007/s00332-017-9437-7
关键词
Koopman operator; Perron-Frobenius operator; Model reduction; Data-driven methods
资金
- Deutsche Forschungsgemeinschaft (DFG) [CRC 1114]
- Einstein Foundation Berlin (Einstein Center ECMath)
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.
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