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In this chapter, we focus our attention on non-intrusive methods for the approximation of an output of a model involving random data, parametrized by a finite set of independent random parameters defined on a suitable probability space. As discussed Chap. 2, we are concerned with models having a unique solution for almost all realizations of the random parameters, so the model can be seen as a surjective mapping from the parameters domain to the image solution space. Because this mapping involves models which are generally complex to solve (for instance PDEs), a natural idea that has been used for a long time is to construct a much simpler mapping, or surrogate model, that approximates the actual complex model. To this end, the so-called non-intrusive methods rely on a set of deterministic model resolutions, corresponding to some specific realizations, to construct the surrogate model. Along this line, a deterministic simulation code can be used as a black-box, which associates to each realization of the parameters the corresponding model output.
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