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Data-driven model reduction and transfer operator approximation

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arxiv 1703.10112 v2 pith:HI5BRHVU submitted 2017-03-29 math.DS

Data-driven model reduction and transfer operator approximation

Stefan Klus , Feliks N\"uske , P\'eter Koltai , Hao Wu , Ioannis Kevrekidis , Christof Sch\"utte , Frank No\'e This is my paper
classification math.DS
keywords methodstransferdata-drivendevelopeddynamicaldynamicsoperatorreduction
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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 (TICA), dynamic mode decomposition (DMD), 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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