  The linear micro-instabilities driving turbulent transport in magnetized
fusion plasmas (as well as the respective nonlinear saturation mechanisms) are
known to be sensitive with respect to various physical parameters
characterizing the background plasma and the magnetic equilibrium. Therefore,
uncertainty quantification is essential for achieving predictive numerical
simulations of plasma turbulence. However, the high computational costs of the
required gyrokinetic simulations and the large number of parameters render
standard Monte Carlo techniques intractable. To address this problem, we
propose a multi-fidelity Monte Carlo approach in which we employ data-driven
low-fidelity models that exploit the structure of the underlying problem such
as low intrinsic dimension and anisotropic coupling of the stochastic inputs.
The low-fidelity models are efficiently constructed via sensitivity-driven
dimension-adaptive sparse grid interpolation using both the full set of
uncertain inputs and subsets comprising only selected, important parameters. We
illustrate the power of this method by applying it to two plasma turbulence
problems with up to $14$ stochastic parameters, demonstrating that it is up to
four orders of magnitude more efficient than standard Monte Carlo methods
measured in single-core performance, which translates into a runtime reduction
from around eight days to one hour on 240 cores on parallel machines.
