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Bayesian analysis of hierarchical multi-fidelity codes.

Abstract : This paper deals with the Gaussian process based approximation of a code which can be run at different levels of accuracy. This method, which is a particular case of co-kriging, allows us to improve a surrogate model of a complex computer code using fast approximations of it. In particular, we focus on the case of a large number of code levels on the one hand and on a Bayesian approach when we have two levels on the other hand. The main results of this paper are a new approach to estimate the model parameters which provides a closed form expression for an important parameter of the model (the scale factor), a reduction of the numerical complexity by simplifying the covariance matrix inversion, and a new Bayesian modelling that gives an explicit representation of the joint distribution of the parameters and that is not computationally expensive. A thermodynamic example is used to illustrate the comparison between 2-level and 3-level co-kriging.
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https://hal.archives-ouvertes.fr/hal-00654716
Contributor : Loic Le Gratiet <>
Submitted on : Monday, September 24, 2012 - 10:25:01 AM
Last modification on : Friday, March 27, 2020 - 3:59:58 AM
Long-term archiving on: : Tuesday, December 25, 2012 - 3:50:12 AM

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  • HAL Id : hal-00654716, version 2
  • ARXIV : 1112.5389

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Loic Le Gratiet. Bayesian analysis of hierarchical multi-fidelity codes.. 2012, pp.RSPA-2011-0742. ⟨hal-00654716v2⟩

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