Bayesian optimization (BO) is a sequential optimization strategy that is increasingly employed in a wide range of areas including materials design. In real world applications, acquiring high-fidelity (HF) data through physical experiments or HF simulations is the major cost component of BO. To alleviate this bottleneck, multi-fidelity (MF) methods are used to forgo the sole reliance on the expensive HF data and reduce the sampling costs by querying inexpensive low-fidelity (LF) sources whose data are correlated with HF samples. However, existing multi-fidelity BO (MFBO) methods operate under the following two assumptions that rarely hold in practical applications: (1) LF sources provide data that are well correlated with the HF data on a global scale, and (2) a single random process can model the noise in the fused data. These assumptions dramatically reduce the performance of MFBO when LF sources are only locally correlated with the HF source or when the noise variance varies across the data sources. In this paper, we dispense with these incorrect assumptions by proposing an MF emulation method that (1) learns a noise model for each data source, and (2) enables MFBO to leverage highly biased LF sources which are only locally correlated with the HF source. We illustrate the performance of our method through analytical examples and engineering problems on materials design.

翻译：贝叶斯优化（BO）是一种序贯优化策略，正越来越多地应用于包括材料设计在内的广泛领域。在实际应用中，通过物理实验或高保真（HF）模拟获取高保真数据是BO的主要成本来源。为缓解这一瓶颈，多保真（MF）方法通过查询与高保真样本数据相关的低成本低保真（LF）源来减少采样成本，从而避免对昂贵的高保真数据的单一依赖。然而，现有MFBO方法通常在以下两个在实际应用中几乎不成立的假设下运行：（1）LF源提供的数据与HF数据全局范围内高度相关；（2）单个随机过程能对融合数据中的噪声进行建模。当LF源仅与HF源局部相关，或不同数据源的噪声方差存在差异时，这些假设会显著降低MFBO的性能。本文通过提出一种MF仿真方法摒弃了这些错误假设，该方法能够（1）为每个数据源学习一个噪声模型，且（2）使MFBO能够利用仅与HF源局部相关的高度有偏LF源。我们通过分析示例和材料设计中的工程问题验证了所提方法的性能。