MODEL REDUCTION FOR LARGE-SCALE SYSTEMS WITH HIGH-DIMENSIONAL PARAMETRIC INPUT SPACE
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Bui-Thanh-2009-MODEL REDUCTION FOR.pdf
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Author(s)
Ghattas, O.
Bui-Thanh, Tan
Willcox, Karen E.
Date Issued
October 2008
Journal
SIAM Journal on Scientific Computing
Publisher
Society for Industrial and Applied Mathematics
Citation
Bui-Thanh, T., K. Willcox, and O. Ghattas. “Model Reduction for Large-Scale Systems with High-Dimensional Parametric Input Space.” SIAM Journal on Scientific Computing 30.6 (2008): 3270-3288. © 2008 Society for Industrial and Applied Mathematics
Version
Final published version
Abstract
A model-constrained adaptive sampling methodology is proposed for the reduction of large-scale systems with high-dimensional parametric input spaces. Our model reduction method uses a reduced basis approach, which requires the computation of high-fidelity solutions at a number of sample points throughout the parametric input space. A key challenge that must be addressed in the optimization, control, and probabilistic settings is the need for the reduced models to capture variation over this parametric input space, which, for many applications, will be of high dimension. We pose the task of determining appropriate sample points as a PDE-constrained optimization problem, which is implemented using an efficient adaptive algorithm that scales well to systems with a large number of parameters. The methodology is demonstrated using examples with parametric input spaces of dimension 11 and 21, which describe thermal analysis and design of a heat conduction fin, and compared with statistically based sampling methods. For these examples, the model-constrained adaptive sampling leads to reduced models that, for a given basis size, have error several orders of magnitude smaller than that obtained using the other methods.
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
http://dx.doi.org/10.1137/070694855
