Abstract:
Model reduction aims to use a low-dimensional dynamical model to capture the key statistical-dynamical properties of a high- or infinite-dimensional process described by a complex dynamical system. A natural approach is to infer a reduced model from simulation data or observation data. A cost effective approach is semi-parametric, in which one derives a family of parametric models and then infers the parameters. In the context of stochastic Burgers equation, we discuss such a semi-parametric approach by parametrizing the projection of the invariant manifolds consisting of the high modes, and possible extensions to general dissipative PDEs. |