Abstract:  Models of nonlinear dynamic phenomena often have many degrees of freedom, but frequently only a small fraction are of direct interest.  This talk concerns a discrete-time, parametric approach to constructing reduced models based on the relevant variables alone [Chorin-Lu 2015].  I will discuss some general issues that arise, and relate the method to the Mori-Zwanzig formalism of nonequilibrium statistical mechanics.  I will illustrate the ideas using a model of spatiotemporal chaos, the Kuramoto-Sivashinsky PDE.