Abstract
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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© 2010 Springer Science+Business Media B.V.
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Le Maître, O.P., Knio, O.M. (2010). Non-intrusive Methods. In: Spectral Methods for Uncertainty Quantification. Scientific Computation. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3520-2_3
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DOI: https://doi.org/10.1007/978-90-481-3520-2_3
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Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-3519-6
Online ISBN: 978-90-481-3520-2
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