  Thanks to computing power increase, the certification and the conception of
complex systems relies more and more on simulation. To this end, predictive
codes are needed, which have generally to be evaluated in a huge number of
input points. When the computational cost of these codes is high, surrogate
models are introduced to emulate the response of these codes. In this paper, we
consider the situation when the system response can be modeled by two nested
computer codes. By two nested computer codes, we mean that some inputs of the
second code are outputs of the first code. More precisely, the idea is to
propose sequential designs to improve the accuracy of the nested code's
predictor by exploiting the nested structure of the codes. In particular, a
selection criterion is proposed to allow the modeler to choose the code to
call, depending on the expected learning rate and the computational cost of
each code. The sequential designs are based on the minimization of the
prediction variance, so adaptations of the Gaussian process formalism are
proposed for this particular configuration in order to quickly evaluate the
mean and the variance of the predictor. The proposed methods are then applied
to examples.
