Bayesian analysis of hierarchical multi-fidelity codes

TL;DR

This paper introduces a Bayesian hierarchical multi-fidelity Gaussian process model that efficiently combines multiple code levels, providing explicit parameter estimation and reduced computational complexity, demonstrated through a thermodynamic example.

Contribution

It presents a novel Bayesian approach for multi-fidelity co-kriging with closed-form parameter estimation and simplified covariance matrix inversion.

Findings

Closed-form expression for the scale factor parameter

Reduced numerical complexity in covariance matrix inversion

Effective modeling of multi-level code approximations

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.