Extended dynamic mode decomposition with dictionary learning: A data-driven adaptive spectral decomposition of the Koopman operator

Qianxiao LiIoannis G Kevrekidis


Numerical approximation methods for the Koopman operator have advanced considerably in the last few years. In particular, data-driven approaches such as dynamic mode decomposition (DMD)51 and its generalization, the extended-DMD (EDMD), are becoming increasingly popular in practical applications. The EDMD improves upon the classical DMD by the inclusion of a flexible choice of dictionary of observables which spans a finite dimensional subspace on which the Koopman operator can be approximated. This enhances the accuracy of the solution reconstruction and broadens the applicability of the Koopman formalism. Although the convergence of the EDMD has been established, applying the method in practice requires a careful choice of the observables to improve convergence with just a finite number of terms. This is especially difficult for high dimensional and highly nonlinear systems. In this paper, we employ ideas from machine learning to improve upon the EDMD method. We develop an iterative approximation algorithm which couples the EDMD with a trainable dictionary represented by an artificial neural network. Using the Duffing oscillator and the Kuramoto Sivashinsky partical differential equation as examples, we show that our algorithm...Continue Reading


May 1, 1931·Proceedings of the National Academy of Sciences of the United States of America·B O Koopman
Jan 3, 2013·Chaos·Marko BudisićIgor Mezić
May 29, 2015·Nature·Yann LeCunGeoffrey Hinton
Apr 2, 2016·Proceedings of the National Academy of Sciences of the United States of America·Steven L BruntonJ Nathan Kutz

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Oct 18, 2019·Proceedings of the National Academy of Sciences of the United States of America·Jiequn HanWeinan E
Nov 25, 2018·Nature Communications·Bethany LuschSteven L Brunton
Jan 3, 2019·The Journal of Chemical Physics·Eugen HruskaCecilia Clementi
Feb 25, 2020·Annual Review of Physical Chemistry·Frank NoéCecilia Clementi
Jun 19, 2019·Nature Communications·Tian XieJeffrey C Grossman
Oct 3, 2019·Chaos·Anastasiya SalovaRaissa M D'Souza
May 1, 2020·Nature Communications·A M Avila, I Mezić
Dec 24, 2020·The Journal of Chemical Physics·Shashank PantPratyush Tiwary
Mar 4, 2021·Chaos·Marvyn Gulina, Alexandre Mauroy
Jun 8, 2021·Chemical Science·Hythem SidkyAndrew L Ferguson
Nov 11, 2020·Journal of Chemical Theory and Computation·Eugen HruskaCecilia Clementi
Nov 5, 2021·Scientific Reports·Craig R GinJ Nathan Kutz

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