A Unified Adaptive Sampling Framework for Multi-Fidelity Modeling and Bayesian Optimization via Latent Variable Gaussian Process
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Multi-fidelity (MF) methods are gaining popularity in response prediction and design optimization by combining information from multiple low-fidelity (LF) models. While most existing MF methods assume a static dataset, adaptive sampling approaches that can allocate resources among different fidelity models are more desirable to achieve higher efficiency in the exploration and exploitation of the design space. Furthermore, most existing MF methods assume hierarchical fidelity levels and fail to explicitly and simultaneously capture the intercorrelation between multiple fidelity levels, making it difficult to perform adaptive sampling. To address this hurdle, we propose a framework that constructs a unified latent embedding for different fidelity models to explicitly capture their correlation postfor adaptive sampling.
In this framework, each adaptive sampling iteration includes two steps: First, we identify the location(s) on high-fidelity (HF) model with the greatest potential improvement, measured by the reduction of uncertainty in global fitting (GF) or expected improvement in Bayesian optimization (BO) . Then, we search for the next sample across all fidelity levels that maximize the improvement per unit cost at the location(s) identified in the first step. This is made possible by using one 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. It enables us to assess how HF/LF sampling candidates will affect HF response with pre-posterior analysis and, therefore, determine the next sample with the best benefit-cost ratio. Through numerical cases, we demonstrate that the proposed method outperforms the state-of-the-art methods in both GF and BO with multi-fidelity models. Moreover, it offers the flexibility to switch between GF and BO by simply changing the acquisition function. The proposed method can significantly expedite the design process for both manufacturing and material systems.