  We link nonlinear manifold learning techniques for data analysis/compression
with model reduction techniques for evolution equations with time scale
separation. In particular, we demonstrate a `"nonlinear extension" of the
POD-Galerkin approach to obtaining reduced dynamic models of dissipative
evolution equations. The approach is illustrated through a reaction-diffusion
PDE, and the performance of different simulators on the full and the reduced
models is compared. We also discuss the relation of this nonlinear extension
with the so-called "nonlinear Galerkin" methods developed in the context of
Approximate Inertial Manifolds.
