1. Notion of metamodel

Finite element simulation is a very powerful technique that can be applied to obtain an approximate solution to the response of a mechanical system. In some cases, predicting the behavior of a system is particularly difficult due to the variability induced by uncertainty. The challenge is to improve the performance of numerical simulations of the mechanical system. Taking these uncertainties into account in system analysis is a complex field, involving the following steps: identification and modeling of uncertainty sources, propagation of uncertainty and post-processing to measure the influence of these uncertainties on system behavior. Recently, the probabilistic modeling of mechanical problems has attracted the attention of a number of researchers. They are looking for more robust models that take into account the random nature of certain parameters: material properties, geometric irregularities,...