Multi-fidelity (MF) methods are gaining popularity for enhancing surrogate modeling and design optimization by incorporating data from various low-fidelity (LF) models. While most existing MF methods assume a fixed dataset, adaptive sampling methods that dynamically allocate resources among fidelity models can achieve higher efficiency in the exploring and exploiting the design space. However, most existing MF methods rely on the hierarchical assumption of fidelity levels or fail to capture the intercorrelation between multiple fidelity levels and utilize it to quantify the value of the future samples and navigate the adaptive sampling. To address this hurdle, we propose a framework hinged on a latent embedding for different fidelity models and the associated pre-posterior analysis to explicitly utilize their correlation for adaptive sampling. In this framework, each infill sampling iteration includes two steps: We first identify the location of interest with the greatest potential improvement using the high-fidelity (HF) model, then we search for the next sample across all fidelity levels that maximize the improvement per unit cost at the location identified in the first step. This is made possible by a single Latent Variable Gaussian Process (LVGP) model that maps different fidelity models into an interpretable latent space to capture their correlations without assuming hierarchical fidelity levels. The LVGP enables us to assess how LF sampling candidates will affect HF response with pre-posterior analysis and determine the next sample with the best benefit-to-cost ratio. Through test cases, we demonstrate that the proposed method outperforms the benchmark methods in both MF global fitting (GF) and Bayesian Optimization (BO) problems in convergence rate and robustness. Moreover, the method offers the flexibility to switch between GF and BO by simply changing the acquisition function.

翻译：多保真（MF）方法通过融合来自不同低保真（LF）模型的数据，在增强代理建模和设计优化方面日益受到关注。尽管现有多数MF方法假设数据集固定，但能动态分配保真模型资源的自适应采样方法可在探索与利用设计空间时实现更高效率。然而，现有多数MF方法或依赖于保真度水平的层次化假设，或未能捕捉多重保真度水平间的相互关联，并利用该关联量化未来样本价值以引导自适应采样。为突破这一瓶颈，我们提出一种基于不同保真模型潜嵌入及其相关前置后验分析的框架，通过显式利用模型间相关性指导自适应采样。在该框架中，每次填充采样迭代包含两个步骤：首先利用高保真（HF）模型定位具有最大潜在改进价值的感兴趣位置，随后在所有保真度水平中搜索能在第一步定位位置处实现每单位成本最大改进的下一个样本。这一过程通过单一潜变量高斯过程（LVGP）模型实现——该模型将不同保真模型映射至可解释潜空间以捕捉其相关性，且无需假设保真度层次结构。LVGP使我们能够通过前置后验分析评估LF采样候选点对HF响应的影响，并确定具有最佳效益成本比的下一个采样点。通过算例验证，所提方法在全局拟合（GF）和贝叶斯优化（BO）问题的收敛速度与鲁棒性方面均优于基准方法。此外，该方法仅需改变采集函数即可灵活切换GF与BO模式。