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 these optima 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 against state-of-the-art multi-objective optimization.

翻译：我们提出了一种新颖的贝叶斯优化（BO）程序，旨在识别具有单一控制参数和多个干扰参数的确定性黑箱计算机模拟的“轮廓最优值”。轮廓最优值将最优响应值表示为控制参数的函数。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值。针对所有参数寻找单一最优值的经典BO方法，无法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方案，以平衡在控制参数上的探索与对轮廓最优值的利用，并利用深层和浅层高斯过程代理模型促进不确定性量化。我们的研究动机来自旋转爆震燃烧发动机中扩散器的计算机模拟，该模拟以各种设计参数为函数返回通过扩散损失的能量。我们旨在根据扩散器长度确定可能的最低能量损失；理解这一关系将有助于做出明智的设计选择。我们的“轮廓贝叶斯优化”程序在多个基准测试中优于传统BO及轮廓优化方法，并在实际应用中证明其性能优于最先进的多目标优化方法。