  The use of surrogate models instead of computationally expensive simulation
codes is very convenient in engineering. Roughly speaking, there are two kinds
of surrogate models: the deterministic and the probabilistic ones. These last
are generally based on Gaussian assumptions. The main advantage of
probabilistic approach is that it provides a measure of uncertainty associated
with the surrogate model in the whole space. This uncertainty is an efficient
tool to construct strategies for various problems such as prediction
enhancement, optimization or inversion.In this paper, we propose a universal
method to define a measure of uncertainty suitable for any surrogate model
either deterministic or probabilistic. It relies on Cross-Validation (CV)
sub-models predictions. This empirical distribution may be computed in much
more general frames than the Gaussian one. So that it is called the Universal
Prediction distribution (UP distribution).It allows the definition of many
sampling criteria. We give and study adaptive sampling techniques for global
refinement and an extension of the so-called Efficient Global Optimization
(EGO) algorithm. We also discuss the use of the UP distribution for inversion
problems. The performances of these new algorithms are studied both on toys
models and on an engineering design problem.
