ON OPTIMAL EXPERIMENTAL DESIGNS FOR SPARSE POLYNOMIAL CHAOS EXPANSIONS
Résumé
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.
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