  Uncertainty quantification (UQ) has received much attention in the literature
in the past decade. In this context, Sparse Polynomial chaos expansions (PCE)
have been shown to be among the most promising methods because of their ability
to model highly complex models at relatively low computational costs. A
least-square minimization technique may be used to determine the coefficients
of the sparse PCE by relying on the so called experimental design (ED), i.e.
the sample points where the original computational model is evaluated. An
efficient sampling strategy is then needed to generate an accurate PCE at low
computational cost. This paper is concerned with the problem of identifying an
optimal experimental design that maximizes the accuracy of the surrogate model
over the whole input space within a given computational budget. A novel
sequential adaptive strategy where the ED is enriched sequentially by
capitalizing on the sparsity of the underlying metamodel is introduced. A
comparative study between several state-of-the-art methods is performed on four
numerical models with varying input dimensionality and computational
complexity. It is shown that the optimal sequential design based on the S-value
criterion yields accurate, stable and computationally efficient PCE.

Methodology