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