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）方法通过整合来自不同低保真（LF）模型的数据，在增强代理模型构建和设计优化方面日益受到关注。尽管现有大多数MF方法假设数据集固定不变，但动态分配资源于不同保真度模型的适应采样方法能够在探索和利用设计空间时实现更高效率。然而，现有大多数MF方法或依赖于保真度层次的层次化假设，或无法捕捉多个保真度层级间的相互关联性并利用该关联性量化未来样本的价值、引导自适应采样。为克服这一障碍，我们提出一个基于潜嵌入框架，该框架针对不同保真度模型及相应的后验分析，显式利用其相关性进行自适应采样。在该框架中，每次填充采样迭代包括两个步骤：首先利用高保真（HF）模型识别具有最大改进潜力的感兴趣位置，随后在所有保真度层级中搜索能在第一步确定的位置上最大化单位成本改进量的下一个样本。这通过单一潜变量高斯过程（LVGP）模型实现，该模型将不同保真度模型映射至可解释的潜空间以捕捉其相关性，无需假设层次化保真度层级。LVGP使我们能够通过后验分析评估LF采样候选对HF响应的影响，并确定具有最佳效益成本比的下一采样点。通过测试案例，我们证明所提方法在多保真全局拟合（GF）和贝叶斯优化（BO）问题中的收敛速率和鲁棒性均优于基准方法。此外，该方法只需更改采集函数即可灵活切换GF与BO模式。