Tag Archives: koopman

Two mode decompositions: POD and DMD

This is a short overview of the Proper Orthogonal and Dynamic/Koopman Mode Decompositions, which are commonly used in analysis of velocity fields of fluid flows. While I worked with the theoretical side of Koopman modes, I never implemented the numerical code myself; I wrote these notes up a I was teaching myself the basics of numerics of these decompositions, and consequently used the notes for two lectures. The notes are based References at the end of the post. Caveat lector: Notes may contain gross oversimplifications — the emphasis was on understanding and not on precision. I welcome your corrections and comments below. (You can always stop by my Van Vleck office if you’re in Madison to discuss any part of this).

UPDATE: I have now posted my own implementation of several algorithms for Koopman mode decompositions. [GitHub]

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Published (with cover image): a review paper on applications of Koopman operators

Chaos: Cover paegUPDATE (2012-12-21): The paper [link] has appeared in AIP Chaos under DOI 10.1063/1.4772195 with one of images making the front page (shown).

UPDATE (2012-12-03): The final draft (arXiv:1206.3164) has been accepted by AIP Chaos and is due to be published in Dec 2012, in Focus issue on 50 years of chaos.

UPDATE (2012-10-14): The revised version of the manuscript is available at arXiv now.

(2012-06-14) A review paper on applications of Koopman operator analysis to dynamical systems, co-authored with Ryan Mohr and Igor Mezić has been submitted for publication to AIP Chaos. The preprint is available on arXiv: Applied Koopmanism.