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）方法因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MF方法大多假设固定数据集，但能够动态分配各保真度模型资源的自适应采样方法，可在探索和开发设计空间时实现更高效率。然而，多数现有MF方法或依赖于保真度层次的层次化假设，或未能捕捉多个保真度之间的相关性并利用其量化未来样本价值以引导自适应采样。为应对这一挑战，我们提出一种框架，该框架基于不同保真度模型的潜嵌入及相应的预-后验分析，显式利用其相关性进行自适应采样。在此框架中，每次填充采样迭代包含两步：首先利用高保真（HF）模型确定具有最大潜在改进潜力的感兴趣位置，随后在第一步确定的位置上，跨所有保真度层级搜索单位成本下改进量最大的下一个样本。这一过程通过单潜变量高斯过程（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，以在无需假设层次化保真度层级的情况下捕捉其相关性。LVGP使我们能够通过预-后验分析评估低保真采样候选对高保真响应的潜在影响，并确定具有最佳性价比的下一个样本。通过算例验证，本文所提方法在收敛速度和鲁棒性方面均优于基准方法，适用于多保真全局拟合（GF）和贝叶斯优化（BO）问题。此外，该方法只需改变采集函数即可灵活切换全局拟合与贝叶斯优化模式。