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arXiv · 1509.09279

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

Fei Lu·Kevin Lin·Alexandre J. Chorin
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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.

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Fei Lu, Kevin Lin, Alexandre J. Chorin. 2015-09-30. Data-based stochastic model reduction for the Kuramoto--Sivashinsky equation. https://arxiv.org/abs/1509.09279

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