Multi-fidelity optimization promises speedups by pairing cheap low-fidelity models with expensive high-fidelity ones, but approximate control variates require covariance information that is usually unknown. The authors propose an active pilot-sampling framework: instead of re-estimating covariances independently at every optimization query, a probabilistic emulator learns how model-output covariances vary across the design domain.
The emulator uses a positive-definite parameterization based on matrix-log-transformed correlations and log standard deviations. Active-learning acquisition functions then allocate pilot samples to designs where covariance information is most uncertain and most relevant to the outer optimization objective, exploiting the fact that covariance structure often varies smoothly across the design space.
The method is demonstrated on a four-branch benchmark and a multi-fidelity Bayesian optimal experimental design application for sensor placement and measurement-time selection in a convection-diffusion system. The authors report improved optimization performance relative to single-fidelity Monte Carlo and simpler pilot-sampling strategies. The paper is by Thomas E. Coons, Aniket Jivani, and Xun Huan (arXiv:2610.27563).