Data-based stochastic model reduction for the Kuramoto--Sivashinsky equation
This work addresses model reduction for high-dimensional spatiotemporal systems with limited data, but the results are incremental and domain-specific.
The authors develop a data-based stochastic reduced model for the Kuramoto-Sivashinsky equation using a NARMAX representation, achieving accurate prediction from limited observations by estimating coefficients for an approximate inertial form.
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.