  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.
