Title: Using Archetypes to Analyze and Control Complex Spatio-Temporal Dynamics
Speaker: Professor Emily Stone
Speaker Info: Utah State University
Archetypal analysis is a new statistical technique for extracting "archetypal patterns" from data sets. It is related to principal component analysis (a.k.a. POD, KL), though its objectives are different: it finds data points on the convex hull of the data set, rather than eigendirections in the data space.Date: Friday, November 7, 1997
A variation of archetypal analysis developed for tracking traveling structures (simple examples being solitons or fronts) has been developed, called "moving archetypes". We have used moving archetypes to reduce a spatially/temporally complex regime from the Kuramoto-Shivashinsky equation to a set of time series, in a manner similar to POD. The time series are then used to enact Ott-Grebogi-Yorke type control on the PDE, returning the solution to a "laminar" regime- a modulated traveling wave. The details of the techniques and the success and limitations of the method will be discussed.