Model Reduction for Large-Scale Systems with High Dimensional Parametric Input Space
Name
ACDL_TR-07-2.pdf
Size
376.09 KB
Format
Adobe PDF
Checksum (MD5)
70aa6b3f947144d4fdc9b1789f3160e0
Author(s)
Bui-Thanh, T.
Willcox, K.
Ghattas, O.
Date Issued
August 2007
Publisher
Aerospace Computational Design Laboratory, Dept. of Aeronautics & Astronautics, Massachusetts Institute of Technology
Series/Report no.
ACDL Technical Reports;ACDL TR-07-2
Abstract
A model-constrained adaptive sampling methodology is proposed for 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 for 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 this example, 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.
Subjects
model reduction
optimization
sampling
heat conduction
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