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

Chaos
Qianxiao LiIoannis G Kevrekidis

Abstract

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

References

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

❮ Previous
Next ❯

Citations

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

❮ Previous
Next ❯

Related Concepts

Trending Feeds

COVID-19

Coronaviruses encompass a large family of viruses that cause the common cold as well as more serious diseases, such as the ongoing outbreak of coronavirus disease 2019 (COVID-19; formally known as 2019-nCoV). Coronaviruses can spread from animals to humans; symptoms include fever, cough, shortness of breath, and breathing difficulties; in more severe cases, infection can lead to death. This feed covers recent research on COVID-19.

Blastomycosis

Blastomycosis fungal infections spread through inhaling Blastomyces dermatitidis spores. Discover the latest research on blastomycosis fungal infections here.

Nuclear Pore Complex in ALS/FTD

Alterations in nucleocytoplasmic transport, controlled by the nuclear pore complex, may be involved in the pathomechanism underlying multiple neurodegenerative diseases including Amyotrophic Lateral Sclerosis and Frontotemporal Dementia. Here is the latest research on the nuclear pore complex in ALS and FTD.

Applications of Molecular Barcoding

The concept of molecular barcoding is that each original DNA or RNA molecule is attached to a unique sequence barcode. Sequence reads having different barcodes represent different original molecules, while sequence reads having the same barcode are results of PCR duplication from one original molecule. Discover the latest research on molecular barcoding here.

Chronic Fatigue Syndrome

Chronic fatigue syndrome is a disease characterized by unexplained disabling fatigue; the pathology of which is incompletely understood. Discover the latest research on chronic fatigue syndrome here.

Evolution of Pluripotency

Pluripotency refers to the ability of a cell to develop into three primary germ cell layers of the embryo. This feed focuses on the mechanisms that underlie the evolution of pluripotency. Here is the latest research.

Position Effect Variegation

Position Effect Variagation occurs when a gene is inactivated due to its positioning near heterochromatic regions within a chromosome. Discover the latest research on Position Effect Variagation here.

STING Receptor Agonists

Stimulator of IFN genes (STING) are a group of transmembrane proteins that are involved in the induction of type I interferon that is important in the innate immune response. The stimulation of STING has been an active area of research in the treatment of cancer and infectious diseases. Here is the latest research on STING receptor agonists.

Microbicide

Microbicides are products that can be applied to vaginal or rectal mucosal surfaces with the goal of preventing, or at least significantly reducing, the transmission of sexually transmitted infections. Here is the latest research on microbicides.

Related Papers

Neural Networks : the Official Journal of the International Neural Network Society
Dino Kosic
International Journal of Neural Systems
Richard Labib, Simon De Montigny
IEEE Transactions on Neural Networks
Emilio Soria-OlivasAntonio J Serrano
© 2021 Meta ULC. All rights reserved