Databased stochastic model reduction for the Kuramoto–Sivashinsky equation
Abstract
In this paper, the problem of constructing databased, 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 discretetime 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:

 Univ. of California, Berkeley, CA (United States). Dept. of Mathematics; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
 Univ. of Arizona, Tucson, AZ (United States). School of Mathematics
 Publication Date:
 Research Org.:
 Lawrence Berkeley National Lab. (LBNL), 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:
 AC0205CH11231; DMS1217065; DMS1418775; DMS1419044
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Physica. D, Nonlinear Phenomena
 Additional Journal Information:
 Journal Volume: 340; Journal ID: ISSN 01672789
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; stochastic parametrization; NARMAX; KuramotoSivashinsky equation; approximate inertial manifold
Citation Formats
Lu, Fei, Lin, Kevin K., and Chorin, Alexandre J. Databased 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. Databased 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 .
"Databased 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 = {Databased 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 databased, 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 discretetime 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 = {2016},
month = {10}
}
Web of Science