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Multi-fidelity Gaussian process regression for computer experiments

Abstract : This work is on Gaussian-process based approximation of a code which can be run at different levels of accuracy. The goal is to improve the predictions of a surrogate model of a complex computer code using fast approximations of it. A new formulation of a co-kriging based method has been proposed. In particular this formulation allows for fast implementation and for closed-form expressions for the predictive mean and variance for universal co-kriging in the multi-fidelity framework, which is a breakthrough as it really allows for the practical application of such a method in real cases. Furthermore, fast cross validation, sequential experimental design and sensitivity analysis methods have been extended to the multi-fidelity co-kriging framework. This thesis also deals with a conjecture about the dependence of the learning curve (ie the decay rate of the mean square error) with respect to the smoothness of the underlying function. A proof in a fairly general situation (which includes the classical models of Gaussian-process based metamodels with stationary covariance functions) has been obtained while the previous proofs hold only for degenerate kernels (ie when the process is in fact finite-dimensional). This result allows for addressing rigorously practical questions such as the optimal allocation of the budget between different levels of codes in the multi-fidelity framework.
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https://tel.archives-ouvertes.fr/tel-00866770
Contributor : Loic Le Gratiet <>
Submitted on : Friday, September 27, 2013 - 10:03:03 AM
Last modification on : Thursday, March 26, 2020 - 9:14:31 PM
Long-term archiving on: : Saturday, December 28, 2013 - 4:29:34 AM

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  • HAL Id : tel-00866770, version 1

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Loic Le Gratiet. Multi-fidelity Gaussian process regression for computer experiments. Autres [stat.ML]. Université Paris-Diderot - Paris VII, 2013. Français. ⟨tel-00866770v1⟩

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