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.
| Identifer | oai:union.ndltd.org:arizona.edu/oai:arizona.openrepository.com:10150/622792 |
| Date | 01 February 2017 |
| Creators | Lu, Fei, Lin, Kevin K., Chorin, Alexandre J. |
| Contributors | School of Mathematics, University of Arizona |
| Publisher | ELSEVIER SCI LTD |
| Source Sets | University of Arizona |
| Language | English |
| Detected Language | English |
| Type | Article |
| Rights | © 2016 Elsevier B.V. All rights reserved. |
| Relation | http://linkinghub.elsevier.com/retrieve/pii/S0167278915301652 |
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