  This paper deals with some of the methodologies used to construct polynomial
surrogate models based on generalized polynomial chaos (gPC) expansions for
applications to uncertainty quantification (UQ) in aerodynamic computations. A
core ingredient in gPC expansions is the choice of a dedicated sampling
strategy, so as to define the most significant scenarios to be considered for
the construction of such metamodels. A desirable feature of the proposed rules
shall be their ability to handle several random inputs simultaneously. Methods
to identify the relative "importance" of those variables or uncertain data
shall be ideally considered as well. The present work is more particularly
dedicated to the development of sampling strategies based on sparsity
principles. Sparse multi-dimensional cubature rules based on general
one-dimensional Gauss-Jacobi-type quadratures are first addressed. These sets
are non nested, but they are well adapted to the probability density functions
with compact support for the random inputs considered in this study. On the
other hand, observing that the aerodynamic quantities of interest (outputs)
depend only weakly on the cross-interactions between the variable inputs, it is
argued that only low-order polynomials shall significantly contribute to their
surrogates. This "sparsity-of-effects" trend prompts the use of reconstruction
techniques benefiting from the sparsity of the outputs, such as compressed
sensing (CS). CS relies on the observation that one only needs a number of
samples proportional to the compressed size of the outputs, rather than their
uncompressed size, to construct reliable surrogate models. The results obtained
with the test case considered in this work corroborate this expected feature.
