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

arXiv: https://arxiv.org/abs/2207.09154 · HTML: https://mlsanity.com/paper/2207.09154/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 42 references that are in the map.
- First posted on arXiv 19 Jul 2022.

## Builds on (most cited first, 9 of 9)

- [Scalable Global Optimization via Local Bayesian Optimization](https://mlsanity.com/paper/1910.01739/) (2019)
- [Max-value Entropy Search for Efficient Bayesian Optimization](https://mlsanity.com/paper/1703.01968/) (2017)
- [Bayesian Optimization in a Billion Dimensions via Random Embeddings](https://mlsanity.com/paper/1301.1942/) (2013)
- [High-Dimensional Bayesian Optimization with Sparse Axis-Aligned Subspaces](https://mlsanity.com/paper/2103.00349/) (2021)
- [High Dimensional Bayesian Optimisation and Bandits via Additive Models](https://mlsanity.com/paper/1503.01673/) (2015)
- [Maximizing acquisition functions for Bayesian optimization](https://mlsanity.com/paper/1805.10196/) (2018)
- [Re-Examining Linear Embeddings for High-Dimensional Bayesian Optimization](https://mlsanity.com/paper/2001.11659/) (2020)
- [The reparameterization trick for acquisition functions](https://mlsanity.com/paper/1712.00424/) (2017)
- [Multi-fidelity Bayesian Optimization with Max-value Entropy Search and its parallelization](https://mlsanity.com/paper/1901.08275/) (2019)

## Built on by (most cited first, 6 of 6)

- [Faster, Cheaper, Better: Multi-Objective Hyperparameter Optimization for LLM and RAG Systems](https://mlsanity.com/paper/2502.18635/) (2025)
- [NUBO: A Transparent Python Package for Bayesian Optimization](https://mlsanity.com/paper/2305.06709/) (2023)
- [On the development of a practical Bayesian optimisation algorithm for expensive experiments and simulations with changing environmental conditions](https://mlsanity.com/paper/2402.03006/) (2024)
- [Multi-Variable Batch Bayesian Optimization in Materials Research: Synthetic Data Analysis of Noise Sensitivity and Problem Landscape Effects](https://mlsanity.com/paper/2504.03943/) (2025)
- [Methods for Multi-objective Optimization PID Controller for quadrotor UAVs](https://mlsanity.com/paper/2509.17423/) (2025)
- [Generative Refinement for Low-Budget Black-Box Optimization](https://mlsanity.com/paper/2607.00691/) (2026)

## Abstract (arXiv)

Bayesian optimization 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 Bayesian optimization algorithms on a range of synthetic test functions to provide general guidance on the design of Bayesian optimization algorithms for specific problems. It investigates the choice of acquisition function, the effect of different numbers of training samples, the exact and Monte Carlo 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 Bayesian optimization 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 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.