Data-based stochastic model reduction for the Kuramoto–Sivashinsky equation

Fei Lu, Kevin K. Lin, Alexandre J. Chorin

Research output: Contribution to journalArticle

23 Scopus citations

Abstract

The 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.

Original languageEnglish (US)
Pages (from-to)46-57
Number of pages12
JournalPhysica D: Nonlinear Phenomena
Volume340
DOIs
StatePublished - Feb 1 2017

Keywords

  • Approximate inertial manifold
  • Kuramoto–Sivashinsky equation
  • NARMAX
  • Stochastic parametrization

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Data-based stochastic model reduction for the Kuramoto–Sivashinsky equation'. Together they form a unique fingerprint.

  • Cite this