  In this paper, we present an adaptive algorithm to construct response surface
approximations of high-fidelity models using a hierarchy of lower fidelity
models. Our algorithm is based on multi-index stochastic collocation and
automatically balances physical discretization error and response surface error
to construct an approximation of model outputs. This surrogate can be used for
uncertainty quantification (UQ) and sensitivity analysis (SA) at a fraction of
the cost of a purely high-fidelity approach. We demonstrate the effectiveness
of our algorithm on a canonical test problem from the UQ literature and a
complex multi-physics model that simulates the performance of an integrated
nozzle for an unmanned aerospace vehicle. We find that, when the input-output
response is sufficiently smooth, our algorithm produces approximations that can
be over two orders of magnitude more accurate than single fidelity
approximations for a fixed computational budget.
