  Quantifying uncertainty in predictive simulations for real-world problems is
of paramount importance - and far from trivial, mainly due to the large number
of stochastic parameters and significant computational requirements. Adaptive
sparse grid approximations are an established approach to overcome these
challenges. However, standard adaptivity is based on global information, thus
properties such as lower intrinsic stochastic dimensionality or anisotropic
coupling of the input directions, which are common in practical applications,
are not fully exploited. We propose a novel structure-exploiting
dimension-adaptive sparse grid approximation methodology using Sobol'
decompositions in each subspace to introduce a sensitivity scoring system to
drive the adaptive process. By employing local sensitivity information, we
explore and exploit the anisotropic coupling of the stochastic inputs as well
as the lower intrinsic stochastic dimensionality. The proposed approach is
generic, i.e., it can be formulated in terms of arbitrary approximation
operators and point sets. In particular, we consider sparse grid interpolation
and pseudo-spectral projection constructed on (L)-Leja sequences. The power and
usefulness of the proposed method is demonstrated by applying it to the
analysis of gyrokinetic microinstabilities in fusion plasmas, one of the key
scientific problems in plasma physics and fusion research. In this context, it
is shown that a 12D parameter space can be scanned very efficiently, gaining
more than an order of magnitude in computational cost over the standard
adaptive approach. Moreover, it allows for the uncertainty propagation and
sensitivity analysis in higher-dimensional plasma microturbulence problems,
which would be almost impossible to tackle with standard screening approaches.
