  Numerical simulation codes are very common tools to study complex phenomena,
but they are often time-consuming and considered as black boxes. For some
statistical studies (e.g. asset management, sensitivity analysis) or
optimization problems (e.g. tuning of a molecular model), a high number of runs
of such codes is needed. Therefore it is more convenient to build a
fast-running approximation - or metamodel - of this code based on a design of
experiments. The topic of this paper is the definition of metamodels for
stochastic codes. Contrary to deterministic codes, stochastic codes can give
different results when they are called several times with the same input. In
this paper, two approaches are proposed to build a metamodel of the probability
density function of a stochastic code output. The first one is based on kernel
regression and the second one consists in decomposing the output density on a
basis of well-chosen probability density functions, with a metamodel linking
the coefficients and the input parameters. For the second approach, two types
of decomposition are proposed, but no metamodel has been designed for the
coefficients yet. This is a topic of future research. These methods are applied
to two analytical models and three industrial cases.
