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International Journal for Uncertainty Quantification
IF: 4.911 5-Year IF: 3.179 SJR: 1.008 SNIP: 0.983 CiteScore™: 5.2

ISSN Print: 2152-5080
ISSN Online: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2020033212
Forthcoming Article

Kernel optimization for Low-Rank Multi-Fidelity Algorithms

Mani Razi
University of Utah
Mike Kirby
Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, Utah, 84112, USA
Akil Narayan
University of Utah

ABSTRACT

One of the major challenges for low-rank multi-fidelity (MF) approaches is the assumption that low-fidelity (LF) and high-fidelity (HF) models admit ``similar'' low-rank kernel representations. Low-rank MF methods have traditionally attempted to exploit low-rank representations of \emph{linear} kernels. However, such linear kernels may not be able to capture low-rank behavior, and they may admit LF and HF kernels that are not similar. Such a situation renders a naive approach to low-rank MF procedures ineffective. In this paper, we propose a novel approach for the selection of a near-optimal kernel function for use in low-rank MF methods. The proposed framework is a two-step strategy wherein: (1) hyperparameters of a library of kernel functions are optimized, and (2) a particular combination of of the optimized kernels is selected, through either a convex mixture (Additive Kernel Approach) or through a data-driven optimization (Adaptive Kernel Approach). The two resulting methods for this generalized framework both utilize only the available inexpensive low-fidelity data and thus no evaluation of high-fidelity simulation model is needed until a kernel is chosen. These proposed approaches are tested on five non-trivial real-world problems including multi-fidelity surrogate modeling for one- and two-species molecular systems, gravitational many-body problem, associating polymer networks, plasmonic nano-particle arrays, and an incompressible flow in channels with stenosis. The results for these numerical experiments demonstrate the numerical stability efficiency of both proposed kernel function selection procedures, as well as high accuracy of their resultant predictive mode