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In this review paper, we will present different data-driven dimensionreduction techniques for dynamical systems that are based on transfer operatortheory as well as methods to approximate transfer operators and theireigenvalues, eigenfunctions, and eigenmodes. The goal is to point outsimilarities and differences between methods developed independently by thedynamical systems, fluid dynamics, and molecular dynamics communities such astime-lagged independent component analysis (TICA), dynamic mode decomposition(DMD), and their respective generalizations. As a result, extensions and bestpractices developed for one particular method can be carried over to otherrelated methods.

Data-driven model reduction and transfer operator approximation