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

Abstract

In this paper, 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. Finally, the broader significance of the results is discussed.

Authors:
 [1]; ORCiD logo [2];  [1]
  1. Univ. of California, Berkeley, CA (United States). Dept. of Mathematics; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
  2. Univ. of Arizona, Tucson, AZ (United States). School of Mathematics
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Univ. of Arizona, Tucson, AZ (United States); Univ. of California, Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC); National Science Foundation (NSF)
OSTI Identifier:
1461977
Alternate Identifier(s):
OSTI ID: 1398711
Grant/Contract Number:  
AC02-05CH11231; DMS-1217065; DMS-1418775; DMS-1419044
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Physica. D, Nonlinear Phenomena
Additional Journal Information:
Journal Volume: 340; Journal ID: ISSN 0167-2789
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; stochastic parametrization; NARMAX; Kuramoto-Sivashinsky equation; approximate inertial manifold

Citation Formats

Lu, Fei, Lin, Kevin K., and Chorin, Alexandre J. Data-based stochastic model reduction for the Kuramoto–Sivashinsky equation. United States: N. p., 2016. Web. doi:10.1016/j.physd.2016.09.007.
Lu, Fei, Lin, Kevin K., & Chorin, Alexandre J. Data-based stochastic model reduction for the Kuramoto–Sivashinsky equation. United States. doi:10.1016/j.physd.2016.09.007.
Lu, Fei, Lin, Kevin K., and Chorin, Alexandre J. Mon . "Data-based stochastic model reduction for the Kuramoto–Sivashinsky equation". United States. doi:10.1016/j.physd.2016.09.007. https://www.osti.gov/servlets/purl/1461977.
@article{osti_1461977,
title = {Data-based stochastic model reduction for the Kuramoto–Sivashinsky equation},
author = {Lu, Fei and Lin, Kevin K. and Chorin, Alexandre J.},
abstractNote = {In this paper, 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. Finally, the broader significance of the results is discussed.},
doi = {10.1016/j.physd.2016.09.007},
journal = {Physica. D, Nonlinear Phenomena},
number = ,
volume = 340,
place = {United States},
year = {Mon Oct 03 00:00:00 EDT 2016},
month = {Mon Oct 03 00:00:00 EDT 2016}
}

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Cited by: 6 works
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