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For practical model-based demands, such as design space exploration anduncertainty quantification (UQ), a high-fidelity model that produces accurateoutputs often has high computational cost, while a low-fidelity model with lessaccurate outputs has low computational cost. It is often possible to constructa bi-fidelity model having accuracy comparable with the high-fidelity model andcomputational cost comparable with the low-fidelity model. This work presentsthe construction and analysis of a non-intrusive (i.e., sample-based)bi-fidelity model that relies on the low-rank structure of the map betweenmodel parameters/uncertain inputs and the solution of interest, if exists.Specifically, we derive a novel, pragmatic estimate for the error committed bythis bi-fidelity model. We show that this error bound can be used to determineif a given pair of low- and high-fidelity models will lead to an accuratebi-fidelity approximation. The cost of this error bound is relatively small anddepends on the solution rank. The value of this error estimate is demonstratedusing two example problems in the context of UQ, involving linear andnon-linear partial differential equations.

Parametric/Stochastic Model Reduction: Low-Rank Representation, Non-Intrusive Bi-Fidelity Approximation, and Convergence Analysis