Multi-fidelity Batch Active Learning for Gaussian Process Classifiers

Many science and engineering problems rely on expensive computational simulations, where a multi-fidelity approach can accelerate the exploration of a parameter space. We study efficient allocation of a simulation budget using a Gaussian Process (GP) model in the binary simulation output case. This paper introduces Bernoulli Parameter Mutual Information (BPMI), a batch active learning algorithm for multi-fidelity GP classifiers. BPMI circumvents the intractability of calculating mutual information in the probability space by employing a first-order Taylor expansion of the link function. We evaluate BPMI against several baselines on two synthetic test cases and a complex, real-world application involving the simulation of a laser-ignited rocket combustor. In all experiments, BPMI demonstrates superior performance, achieving higher predictive accuracy for a fixed computational budget.