A methodology for fitting and validating metamodels in simulation

However, in the environmental domain, as in many areas of application, the numerical model outputs are often spatial maps, which may also vary with time.In this paper, we introduce an inno-vative method to obtain a spatial map of Sobol ’ indices with a minimal number of numerical model computations. Global sensitivity analysis of complex numerical models can be performed by calculating variance-based importance measures of the input variables, such as the Sobol indices.However, these techniques, requiring a large number of model evaluations, are often unacceptable for time expensive computer c ..." Global sensitivity analysis of complex numerical models can be performed by calculating variance-based importance measures of the input variables, such as the Sobol indices.

The efficiency of this algorithm is compared to the efficiency of other existing algorithms on an analytical test case.

However, these techniques, requiring a large number of model evaluations, are often unacceptable for time expensive computer codes.

A well known and widely used decision consists in replacing the computer code by a metamodel, predicting the model responses with a negligible computation time and rending straightforward the estimation of Sobol indices.

These approximations introduce a new element of uncertainty during design optimization, and there is a need to develop ef � cient methods to assess metamodel validity.

We investigate computationally inexpensive assessment methods for metamodel validation based on leave-k-out cross validation and develop guidelines for selecting k for different types of metamodels.

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Comparisons between the two estimates, made on analytical examples, show the superiority of the second approach in terms of convergence and robustness.

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