Investigating Bayesian optimization for expensive-to-evaluate black box functions: application in fluid dynamics
File(s)
Published version
Author(s)
Type
Journal Article
Abstract
Bayesian optimization (BO) provides an effective method to optimize expensive-to-evaluate black box functions. It has been widely applied to problems in many fields, including notably in computer science, e.g., in machine learning to optimize hyperparameters of neural networks, and in engineering, e.g., in fluid dynamics to optimize control strategies that maximize drag reduction. This paper empirically studies and compares the performance and the robustness of common BO algorithms on a range of synthetic test functions to provide general guidance on the design of BO algorithms for specific problems. It investigates the choice of acquisition function, the effect of different numbers of training samples, the exact and Monte Carlo (MC) based calculation of acquisition functions, and both single-point and multi-point optimization. The test functions considered cover a wide selection of challenges and therefore serve as an ideal test bed to understand the performance of BO to specific challenges, and in general. To illustrate how these findings can be used to inform a Bayesian optimization setup tailored to a specific problem, two simulations in the area of computational fluid dynamics (CFD) are optimized, giving evidence that suitable solutions can be found in a small number of evaluations of the objective function for complex, real problems. The results of our investigation can similarly be applied to other areas, such as machine learning and physical experiments, where objective functions are expensive to evaluate and their mathematical expressions are unknown.
Date Issued
2022-12-08
Date Acceptance
2022-11-11
Citation
Frontiers in Applied Mathematics and Statistics, 2022, 8
ISSN
2297-4687
Publisher
Frontiers Media S.A.
Journal / Book Title
Frontiers in Applied Mathematics and Statistics
Volume
8
Copyright Statement
© 2022 Diessner, O’Connor, Wynn, Laizet, Guan, Wilson and Whalley. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
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Subjects
Bayesian optimization
black box function
computer simulation
fluid dynamics
Gaussian Process
Mathematics
Mathematics, Interdisciplinary Applications
Physical Sciences
Science & Technology
turbulent drag reduction
Publication Status
Published
Article Number
1076296
Date Publish Online
2022-12-08