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Surrogate models for the uncertainty quantification of nested phenomena

Simulation is increasingly used for the sensitivity analysis and the uncertainty quantification of complex systems. Large sets of code evaluations are generally needed to carry out such numerical procedures. When the computational cost associated with one particular evaluation of the code is high, such direct approaches based on the computer simulations only can be not affordable. Surrogate models have therefore to be introduced to interpolate the information given by a fixed set of code evaluations to the whole input space. When confronted to deterministic mappings, the Gaussian process-based regression (GPR), or kriging, presents a good compromise between complexity, efficiency and error control. Such a method considers that the quantity of interest of the system is a particular realization of a Gaussian stochastic process that has to be determined. This work presents some recent developments on the adaptation of this GPR formalism for the analysis of two nested codes. By nested code, we mean that at least one output of the first code is an input of the second code. This nested configuration is actually very frequent in the modeling of complex systems (Let’s think about the weak coupling in the modeling of fluid-structure interaction for instance). With respect to the available information about the nested phenomenon of interest, adapted surrogate models will be proposed. The interest of such specific constructions will finally be illustrated on a series of examples.

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