  Multi-fidelity methods leverage low-cost surrogate models to speed up
computations and make occasional recourse to expensive high-fidelity models to
establish accuracy guarantees. Because surrogate and high-fidelity models are
used together, poor predictions by surrogate models can be compensated with
frequent recourse to high-fidelity models. Thus, there is a trade-off between
investing computational resources to improve the accuracy of surrogate models
versus simply making more frequent recourse to expensive high-fidelity models;
however, this trade-off is ignored by traditional modeling methods that
construct surrogate models that are meant to replace high-fidelity models
rather than being used together with high-fidelity models. This work considers
multi-fidelity importance sampling and theoretically and computationally trades
off increasing the fidelity of surrogate models for constructing more accurate
biasing densities and the numbers of samples that are required from the
high-fidelity models to compensate poor biasing densities. Numerical examples
demonstrate that such context-aware surrogate models for multi-fidelity
importance sampling have lower fidelity than what typically is set as tolerance
in traditional model reduction, leading to runtime speedups of up to one order
of magnitude in the presented examples.
