Model-constrained optimization methods for reduction of parameterized large-scale systems

Most model reduction techniques employ a projection framework that utilizes a reduced-space basis. The basis is usually formed as the span of a set of solutions of the large-scale system, which are computed for selected values (samples) of input parameters and forcing inputs. In existing model reduction techniques, choosing where and how many samples to generate has been, in general, an ad-hoc process. A key challenge is therefore how to systematically sample the input space, which is of high dimension for many applications of interest. This thesis proposes and analyzes a model-constrained greedy-based adaptive sampling approach in which the parametric input sampling problem is formulated as an optimization problem that targets an error estimation of reduced model output prediction. The method solves the optimization problem to find a locally-optimal point in parameter space where the error estimator is largest, updates the reduced basis with information at this optimal sample location, forms a new reduced model, and repeats the process. Therefore, we use a systematic, adaptive error metric based on the ability of the reduced-order model to capture the outputs of interest in order to choose the snapshot locations that are locally the worst case scenarios.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Aeronautics and Astronautics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2007

Author dc:creator

• Bui-Thanh, Tan

Advisor dc:contributor.advisor

• Karen E. Willcox.

• Aeronautics and Astronautics.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/40305

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/40305