Sampling, Metamodeling, and Sensitivity Analysis of Numerical Simulators with Functional Stochastic Inputs

Abstract

In this paper, we define a new methodology to perform sensitivity analysis of a computer simulation code in a particular case, whose study is motivated by a nuclear reliability application. This particular framework is characterized by three features. The first feature is that this kind of code is computationally expensive, which limits the number of available code evaluations. Second, code inputs are scalar and functional parameters, and the functional ones can be mutually dependent. Third, the probability distribution of the functional inputs is not known; only a sample of their realizations is available. The proposed methodology is a combination and an adaptation of existing methods. First, the functional input uncertainty is quantified via a functional decomposition combined with a sparse Gaussian mixture model. From this obtained probability density function, a method is proposed to sample uniformly both the functional and the scalar input variation domain. Then, variance-based sensitivity indices ar...