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arXiv · 1703.10112

Data-driven model reduction and transfer operator approximation

Stefan Klus·Feliks Nüske·Péter Koltai·Hao Wu·Ioannis Kevrekidis·Christof Schütte·Frank Noé
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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 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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Stefan Klus, Feliks Nüske, Péter Koltai, Hao Wu, Ioannis Kevrekidis, Christof Schütte, Frank Noé. 2017-09-18. Data-driven model reduction and transfer operator approximation. https://doi.org/10.1007/s00332-017-9437-7

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