We propose a novel Bayesian optimization (BO) procedure aimed at identifying the ``profile optima'' of a deterministic black-box computer simulation that has a single control parameter and multiple nuisance parameters. The profile optima capture the optimal response values as a function of the control parameter. Our objective is to identify them across the entire plausible range of the control parameter. Classic BO, which targets a single optimum over all parameters, does not explore the entire control parameter range. Instead, we develop a novel two-stage acquisition scheme to balance exploration across the control parameter and exploitation of the profile optima, leveraging deep and shallow Gaussian process surrogates to facilitate uncertainty quantification. We are motivated by a computer simulation of a diffuser in a rotating detonation combustion engine, which returns the energy lost through diffusion as a function of various design parameters. We aim to identify the lowest possible energy loss as a function of the diffuser's length; understanding this relationship will enable well-informed design choices. Our ``profile Bayesian optimization'' procedure outperforms traditional BO and profile optimization methods on a variety of benchmarks and proves effective in our motivating application.

翻译：本文提出了一种新颖的贝叶斯优化（BO）方法，旨在识别具有单一控制参数和多个干扰参数的确定性黑盒计算机模拟的“剖面最优解”。剖面最优解描述了最优响应值作为控制参数的函数关系。我们的目标是在控制参数的整个合理范围内识别这些最优解。传统的贝叶斯优化方法以所有参数上的单一最优解为目标，无法充分探索整个控制参数范围。为此，我们开发了一种新颖的两阶段采集策略，以平衡控制参数范围的探索与剖面最优解的利用，并借助深度和浅层高斯过程代理模型来促进不确定性量化。本研究的动机源于旋转爆震燃烧发动机中扩散器的计算机模拟，该模拟返回通过扩散损失的能量作为各种设计参数的函数。我们的目标是识别扩散器长度函数下的最低可能能量损失；理解这种关系将有助于做出明智的设计决策。我们的“剖面贝叶斯优化”方法在多种基准测试中优于传统贝叶斯优化和剖面优化方法，并在实际应用中证明了其有效性。