# 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:

- 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); 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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