Investigating Bayesian optimization for expensive-to-evaluate black box functions: Application in fluid dynamics

Mike Diessner*, Joseph O'Connor, Andrew Wynn, Sylvain Laizet, Yu Guan, Kevin Wilson*, Richard D. Whalley*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

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.

Original languageEnglish
Article number1076296
JournalFrontiers in Applied Mathematics and Statistics
Volume8
DOIs
Publication statusPublished - 8 Dec 2022

Keywords / Materials (for Non-textual outputs)

  • Bayesian optimization
  • black box function
  • computer simulation
  • fluid dynamics
  • Gaussian Process
  • turbulent drag reduction

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