A Latent Variable Approach for Non-Hierarchical Multi-Fidelity Adaptive Sampling

Multi-fidelity (MF) methods are gaining popularity for enhancing surrogate modeling and design optimization by incorporating data from both high- and various low-fidelity (LF) models. While most existing MF methods assume a fixed training set, adaptive sampling methods that dynamically allocate resources among models with different fidelities can achieve higher efficiency in the exploration and exploitation of the design space. However, these methods either rely on the hierarchical assumption of fidelity levels or fail to capture their intercorrelation which is critical in quantifying the benefit of future samples for the adaptive sampling. To address this hurdle, we propose an MF adaptive sampling framework hinged on a latent embedding for different fidelity models and an associated pre-posterior analysis to explicitly utilize their correlations to quantify the benefit of the candidate samples as the sampling criteria. In this framework, each infill sampling iteration includes two steps: First, we identify the HF location of interest with the greatest potential improvement of the high-fidelity (HF) model, and then search for the next sample across all fidelity levels that maximizes 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 any hierarchy between fidelity levels. The LVGP enables us to assess how LF sampling candidates will affect HF response with a pre-posterior analysis and determine the next sample with the best benefit-to-cost ratio. Furthermore, the proposed method offers the flexibility to switch between global fitting (GF) and Bayesian optimization (BO) by simply changing the acquisition function. Through test cases, we demonstrate that our method outperforms state-of-the-art methods in both MF GF and BO problems in the rate of convergence and robustness.