Kriging-sparse Polynomial Dimensional Decomposition surrogate model with adaptive refinement

Andrea Francesco Cortesi (1) , Ghina Jannoun (2) , Pietro Marco Congedo (3, 4)

1 CARDAMOM - Certified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts
2 CESI - CESI : groupe d’Enseignement Supérieur et de Formation Professionnelle
3 DeFI - Shape reconstruction and identification
4 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

Uncertainty Quantification and Sensitivity Analysis problems are made more difficult in the case of applications involving expensive computer simulations. This is because a limited amount of simulations is available to build a sufficiently accurate metamodel of the quantities of interest. In this work, an algorithm for the construction of a low-cost and accurate metamodel is proposed, having in mind computationally expensive applications. It has two main features. First, Universal Kriging is coupled with sparse Polynomial Dimensional Decomposition (PDD) to build a metamodel with improved accuracy. The polynomials selected by the adaptive PDD representation are used as a sparse basis to build a Universal Kriging surrogate model. Secondly, a numerical method, derived from anisotropic mesh adaptation, is formulated in order to adaptively insert a fixed number of new training points to an existing Design of Experiments. The convergence of the proposed algorithm is analyzed and assessed on different test functions with an increasing size of the input space. Finally, the algorithm is used to propagate uncertainties in two high-dimensional real problems related to the atmospheric reentry.

Mots clés: Surrogate modeling; Universal kriging; Sparse polynomial dimensional decomposition; Anisotropic adaptive meshing; Adaptive refinement

Domaines: Dynamique des Fluides [physics.flu-dyn]

Andrea Francesco Cortesi, Ghina Jannoun, Pietro Marco Congedo. Kriging-sparse Polynomial Dimensional Decomposition surrogate model with adaptive refinement. Journal of Computational Physics, inPress, 380, pp.212-242. ⟨10.1016/j.jcp.2018.10.051⟩. ⟨hal-01914383⟩