Kriging-sparse Polynomial Dimensional Decomposition surrogate model with adaptive refinement

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.