  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.
