Higher order dynamic mode decomposition

Le Clainche Martinez, Soledad and Vega De Prada, Jose Manuel (2017). Higher order dynamic mode decomposition. "SIAM Journal on Applied Dynamical Systems", v. 16 (n. 2); pp. 882-925. ISSN 1536-0040. https://doi.org/10.1137/15M1054924.

Description

Title: Higher order dynamic mode decomposition
Author/s:
  • Le Clainche Martinez, Soledad
  • Vega De Prada, Jose Manuel
Item Type: Article
Título de Revista/Publicación: SIAM Journal on Applied Dynamical Systems
Date: 2017
ISSN: 1536-0040
Volume: 16
Subjects:
Freetext Keywords: Dynamic mode decomposition; Koopman operator; delayed snapshots; nonlinear dynamical systems; transient dynamics; quasi-periodic attractors; complex Ginzburg–Landau equation; thermal convection in spherical shells
Faculty: E.T.S. de Ingeniería Aeronáutica y del Espacio (UPM)
Department: Matemática Aplicada a la Ingeniería Aeroespacial
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

This paper deals with an extension of dynamic mode decomposition (DMD), which is appropriate to treat general periodic and quasi-periodic dynamics, and transients decaying to periodic and quasiperiodic attractors, including cases (not accessible to standard DMD) that show limited spatial complexity but a very large number of involved frequencies. The extension, labeled as higher order dynamic mode decomposition, uses time-lagged snapshots and can be seen as superimposed DMD in a sliding window. The new method is illustrated and clarified using some toy model dynamics, the Stuart–Landau equation, and the Lorenz system. In addition, the new method is applied to (and its robustness is tested in) some permanent and transient dynamics resulting from the complex Ginzburg–Landau equation (a paradigm of pattern forming systems), for which standard DMD is seen to only uncover trivial dynamics, and the thermal convection in a rotating spherical shell subject to a radial gravity field.

More information

Item ID: 50185
DC Identifier: http://oa.upm.es/50185/
OAI Identifier: oai:oa.upm.es:50185
DOI: 10.1137/15M1054924
Official URL: https://epubs.siam.org/doi/abs/10.1137/15M1054924?journalCode=sjaday
Deposited by: Memoria Investigacion
Deposited on: 01 Aug 2018 10:46
Last Modified: 01 Aug 2018 10:46
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