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MULTIFIDELITY DIMENSION REDUCTION VIA ACTIVE
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DOI：10.1137/18M1214123.png)
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Abstract
En 中文
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.
Keywords:
dimension reduction
multifidelity
gradient-based
active subspace
intrinsic dimension
effective rank
matrix Bernstein inequality
control variate
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