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Thanks to computing power increase, the certification and the conception ofcomplex systems relies more and more on simulation. To this end, predictivecodes are needed, which have generally to be evaluated in a huge number ofinput points. When the computational cost of these codes is high, surrogatemodels are introduced to emulate the response of these codes. In this paper, weconsider the situation when the system response can be modeled by two nestedcomputer codes. By two nested computer codes, we mean that some inputs of thesecond code are outputs of the first code. More precisely, the idea is topropose sequential designs to improve the accuracy of the nested code'spredictor by exploiting the nested structure of the codes. In particular, aselection criterion is proposed to allow the modeler to choose the code tocall, depending on the expected learning rate and the computational cost ofeach code. The sequential designs are based on the minimization of theprediction variance, so adaptations of the Gaussian process formalism areproposed for this particular configuration in order to quickly evaluate themean and the variance of the predictor. The proposed methods are then appliedto examples.

Efficient sequential experimental design for surrogate modeling of nested codes