Loic Le Gratiet

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1 Abstract This paper deals with the learning curve in a Gaussian process regression framework. The learning curve describes the generalization error of the Gaussian process used for the regression. The main result is the proof of a theorem giving the generalization error for a large class of correlation kernels and for any dimension when the number of(More)
abstract We consider in this paper the problem of building a fast-running approximation-also called surrogate model-of a complex computer code. The co-kriging based surrogate model is a promising tool to build such an approximation when the complex computer code can be run at different levels of accuracy. We present here an original approach to perform a(More)
We consider in this paper the problem of building a fast-running approximation—also called surrogate model—of a complex computer code. The co-kriging based surrogate model is a promising tool to build such an approximation when the complex computer code can be run at different levels of accuracy. We present here an original approach to perform a(More)
This paper deals with the learning curve in a Gaussian process regression framework. The learning curve describes the generalization error of the Gaussian process used for the regression. The main result is the proof of a theorem giving the generalization error for a large class of correlation kernels and for any dimension when the number of observations is(More)
1 Abstract Stochastic simulators such as Monte-Carlo estimators are widely used in science and engineering to study physical systems through their probabilistic representation. Global sensitivity analysis aims to identify the input parameters which have the most important impact on the output. A popular tool to perform global sensitivity analysis is the(More)
Complex computer codes are widely used in science to model physical systems. Sensitivity analysis aims to measure the contributions of the inputs on the code output variability. An efficient tool to perform such analysis are the variance-based methods which have been recently investigated in the framework of dependent inputs. One of their issue is that they(More)
1 Abstract Kriging-based surrogate models have become very popular during the last decades to approximate a computer code output from few simulations. In practical applications, it is very common to sequentially add new simulations to obtain more accurate approximations. We propose in this paper a method of kriging-based sequential design which combines(More)
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