Data-based stochastic model reduction for the Kuramoto–Sivashinsky equation
AffiliationSchool of Mathematics, University of Arizona
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PublisherELSEVIER SCI LTD
CitationData-based stochastic model reduction for the Kuramoto–Sivashinsky equation 2017, 340:46 Physica D: Nonlinear Phenomena
JournalPhysica D: Nonlinear Phenomena
Rights© 2016 Elsevier B.V. All rights reserved.
Collection InformationThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at firstname.lastname@example.org.
AbstractThe problem of constructing data-based, predictive, reduced models for the Kuramoto–Sivashinsky equation is considered, under circumstances where one has observation data only for a small subset of the dynamical variables. Accurate prediction is achieved by developing a discrete-time stochastic reduced system, based on a NARMAX (Nonlinear Autoregressive Moving Average with eXogenous input) representation. The practical issue, with the NARMAX representation as with any other, is to identify an efficient structure, i.e., one with a small number of terms and coefficients. This is accomplished here by estimating coefficients for an approximate inertial form. The broader significance of the results is discussed.
Note24 month embargo; Available online 3 October 2016
VersionFinal accepted manuscript
SponsorsNational Science Foundation [DMS-1217065, DMS-1418775, DMS-1419044]; U.S. Department of Energy [DE-AC02-05CH11231]; National Science Foundation