Data-driven Model Reduction by Wiener Projection
Many models used in industry are large and require a run (often repeated runs) of a full, computationally expensive model to produce results of tolerable accuracy. These systems may have limited data available, in that the number of variables that are observable is small, or the frequency of observation is low. Here we discuss a technique of model reduction informed by data from, as well as the dynamical equations of, the full model. The technique makes use of results from signal processing as well as statistical mechanics. The method for producing the reduced model uses the so-called Wiener projection. In this talk I provide a brief background on the Wiener filter and spectral factorization techniques and then describe the method of Wiener projection. Then I present a battery of examples and culminate with a discussion on how I have been applying this method to the Kuramoto-Sivashinsky equation.