ON OPTIMAL EXPERIMENTAL DESIGNS FOR SPARSE POLYNOMIAL CHAOS EXPANSIONS

Noura Fajraoui (1) , S Marelli (1) , B Sudret (2, 1)

1 Chair of Risk, Safety and Uncertainty Quantification [ETH Zurich]
2 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques

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.

Mots clés: Optimal Experimental Design; Sparse Polynomial Chaos Expansions; Sequential Experimental design

Domaines: Applications [stat.AP]; Méthodologie [stat.ME]

Noura Fajraoui, S Marelli, B Sudret. ON OPTIMAL EXPERIMENTAL DESIGNS FOR SPARSE POLYNOMIAL CHAOS EXPANSIONS. [Research Report] ETH Zurich, Chair of Risk, Safety and Uncertainty Quantifi- cation, Stefano-Franscini-Platz 5, 8093 Zurich, Switzerland. 2016. ⟨hal-01571319⟩