Title: Symmetry Preserving Principle Component Analysis for Dynamical Systems

Speaker: Danny Sorensen, Department of Computational and Applied Mathematics, Rice University
                              
Date/Time: Tuesday, June 21, 2005, 10:00-11:00 am

Location: Building 980, Room 24 (Sandia NM)

Brief Abstract: Model reduction seeks to replace a large-scale system of differential or difference equations by a system of substantially lower dimension, that ideally, has the same response characteristics as the original system, yet requires far less computational resources for realization. Such large-scale systems arise in structural analysis, circuit simulation, protein dynamics, spatial discretization of certain time dependent PDE control systems and in many other applications.

Principle Component Analysis based upon the singular value decomposition of a discrete trajectory is central to a number of important model reduction methods in both linear and nonlinear settings.  This talk will introduce the ideas of model reduction for dynamical systems in this context and give a brief introduction to methods for large scale problems.
 
In the molecular dynamics of proteins, there are often symmetry conditions on the molecular conformations that should be respected.  We shall introduce a relatively new technique for a symmetry preserving SVD suitable for a reduced basis analysis in molecular dynamics that respects known symmetries.