Scheduled Talk - September 26, 2011 - [ 3:00PM in DCH 1064 ]

Karen Willcox
Department of Aeronautics & Astronautics
Massachusetts Institute of Technology

"Model Reduction for Large-Scale Systems: Efficient Approaches for Problems with High-Dimensional Parameter Spaces"

Abstract:
Recent years have seen considerable advancements in the field of model reduction for large-scale systems. In particular, new projection-based methods have been developed for nonlinear and parametrically-varying systems, opening up a broad new class of potential applications. Problems with large parameter dimension present a significant opportunity for model reduction to accelerate solution of large-scale systems with applications in optimization, inverse problems and uncertainty quantification. However, large parameter dimension also poses a significant challenge, since most model reduction methods rely on sampling the parameter space to build the reduced-space basis. This talk highlights recent progress on model reduction for large-scale problems with many parameters. Our approaches use optimization methods to guide the selection of samples over the parameter space in an adaptive manner. We also show how reduced basis approximations of the state space can be extended to reduce the dimension of the parameter space. We demonstrate our methods in the context of applications in optimization, inverse problems and uncertainty quantification with a variety of engineering examples.