Bayesian Hierarchical Emulators for Multi-Level Models: BayHEm

TL;DR

This paper introduces BayHEm, a Bayesian hierarchical approach to multi-level Gaussian process emulators that efficiently leverages hierarchies of models to improve top-level emulation with fewer runs.

Contribution

It proposes a novel Bayesian hierarchical structure for GPs that shares information across model fidelity levels, reducing parameters and improving accuracy.

Findings

Enhanced emulation accuracy at high fidelity levels

Reduced number of runs needed for top-level emulation

Effective sharing of information across model hierarchies

Abstract

Decision making often uses complex computer codes run at the exa-scale (10e18 flops). Such computer codes or models are often run in a hierarchy of different levels of fidelity ranging from the basic to the very sophisticated. The top levels in this hierarchy are expensive to run, limiting the number of possible runs. To make use of runs over all levels, and crucially improve emulation at the top level, we use multi-level Gaussian process emulators (GPs). We will present a new method of building GP emulators from hierarchies of models. In order to share information across the different levels, l=1,...,L, we define the form of the prior of the l+1th level to be the posterior of the lth level, hence building a Bayesian hierarchical structure for the top Lth level. This enables us to not only learn about the GP hyperparameters as we move up the multi-level hierarchy, but also allows us to limit the total number of parameters in the full model, whilst maintaining accuracy.