Surrogating the response PDF of stochastic simulators using generalized lambda distributions

Abstract

Computer simulation is used in all fields of applied science and engineering to represent complex systems and be able to make predictions about their behaviour. Kriging and polynomial chaos (PC) expansions are nowadays well-established techniques to surrogate complex models when a large number of runs is required, which is the case in the context of optimization or uncertainty quantification. Classically, computer models are deterministic, in the sense that they produce the exact same output quantities of interest when run twice with the same parameters. In contrast, in this paper, we are interested in stochastic simulators, for which there are extra internal sources of randomness in the computer code, so that two runs produce different results. Of interest is the construction of a surrogate that predicts the response probability density function (PDF) for any input parameter set. We propose a two-step approach based on a local inference of the response PDF in each point of an experimental design using generalized lambda distributions, the distribution parameters of which being represented in a second step by PC expansions. Two versions of the algorithm are proposed and compared on two analytical examples, which allow to assess their respective accuracy.