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.
Future talks in Scientific Computing Seminar
Feb. 11: Alexei Lozinski, IACS, Ecole Polytechnique Fédérale de Lausanne, Switzerland
Feb. 17: Hans-Joachim Bungartz, IPVS, Universitaet Stuttgart, Germany.
Mar. 3: Bernd Simeon, Center of Mathematics, Munich University of Technology, Germany.
Apr. 28: Gene H Golub, Department of Computer Science, Stanford University.
This seminar is easily accessible to persons with disabilities. For more information or for assistance, please contact the Mathematics Department at 743-3500.