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.
Cite
@article{arxiv.1112.5389,
title = {Bayesian analysis of hierarchical multi-fidelity codes},
author = {Loic Le Gratiet},
journal= {arXiv preprint arXiv:1112.5389},
year = {2012}
}