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Data-Driven Model Reduction and Transfer Operator Approximation.

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Title: Data-Driven Model Reduction and Transfer Operator Approximation.
Authors: Klus, Stefan1 stefan.klus@fu-berlin.de, Nüske, Feliks1, Koltai, Péter1, Wu, Hao1, Kevrekidis, Ioannis2,3, Schütte, Christof1,3, Noé, Frank1
Source: Journal of Nonlinear Science. Jun2018, Vol. 28 Issue 3, p985-1010. 26p.
Subjects: Dynamical systems, Transfer operators, Molecular dynamics, Independent component analysis, Eigenfunctions
Abstract: 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. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
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Abstract: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 <italic>time-lagged independent component analysis</italic>, <italic>dynamic mode decomposition</italic>, and their respective generalizations. As a result, extensions and best practices developed for one particular method can be carried over to other related methods. [ABSTRACT FROM AUTHOR]
ISSN:09388974
DOI:10.1007/s00332-017-9437-7