Multifidelity Dimension Reduction via Active Subspaces
Name
18m1214123.pdf
Description
Published version
Size
1.25 MB
Format
Adobe PDF
Checksum (MD5)
ca13e53394b4238ba55700dff8510723
Author(s)
Lam, Remi R
Zahm, Olivier
Marzouk, Youssef M
Willcox, Karen E
Date Issued
2020
Journal
SIAM Journal on Scientific Computing
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Version
Final published version
Abstract
© 2020 Remi Lam, Olivier Zahm, Youssef Marzouk, Karen Willcox. We propose a multifidelity dimension reduction method to identify a low-dimensional structure present in many engineering models. The structure of interest arises when functions vary primarily on a low-dimensional subspace of the high-dimensional input space, while varying little along the complementary directions. Our approach builds on the gradient-based methodology of active subspaces, and exploits models of different fidelities to reduce the cost of performing dimension reduction through the computation of the active subspace matrix. We provide a nonasymptotic analysis of the number of gradient evaluations sufficient to achieve a prescribed error in the active subspace matrix, both in expectation and with high probability. We show that the sample complexity depends on a notion of intrinsic dimension of the problem, which can be much smaller than the dimension of the input space. We illustrate the benefits of such a multifidelity dimension reduction approach using numerical experiments with input spaces of up to two thousand dimensions.
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.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1137/18M1214123
