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Variable fidelity expected improvement for Cokriging

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posted on 2022-10-10, 04:00 authored by Duncan Crowley

This thesis explores multi-fidelity, surrogate-based, Bayesian optimisation. These are a series of techniques that solve optimisation problems with a high cost for evaluating the objective function. A multi-fidelity approach allows for the incorporation of cheap approximations of the objective function. The multi-fidelity data allows us to fit a Cokriging surrogate model, this is a type of surrogate model designed for multi-fidelity data. A Cokriging model is a more accurate model than one that is fitted with only a small amount of high-fidelity data. A more accurate surrogate model allows for better points to be acquired by the Bayesian optimisation algorithm's acquisition function. In this regard, we have developed a variable fidelity acquisition function that works with the Cokriging model based on a similar approach developed for a hierarchical Kriging model. This new approach performs mor efficiently when compared with the traditional single fidelity acquisition function. Further, we demonstrated viable stopping criteria for a Bayesian optimisation algorithm, an area that is lacking in the literature. Finally, we derived a parallel variable fidelity acquisition function that performed as well as a sequential variable fidelity acquisition function allowing for the use of parallel computing.


Table of Contents

1 Introduction -- 2 Literature Review -- 3 Methodology -- 4 Experimental Design and Results -- 5 Discussion -- 6 Conclusion -- A Additional Resources -- References


A thesis submitted to Macquarie University for the degree of Masters of Research

Awarding Institution

Macquarie University

Degree Type

Thesis MRes


Thesis (MRes), Department of Mathematics and Statistics, Faculty of Science and Engineering, Macquarie University

Department, Centre or School

Department of Mathematics and Statistics

Year of Award


Principal Supervisor

David Bulger


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