Multi-fidelity Batch Active Learning for Gaussian Process Classifiers

TL;DR

This work tackles the challenge of efficiently mapping ignition probabilities in bi-fidelity, binary-output simulations under a fixed budget. It introduces Bernoulli Parameter Mutual Information (BPMI), a batch acquisition function that directly targets information gain on Bernoulli probabilities by linearizing the probit link, enabling tractable MI estimation within a bi-fidelity Gaussian Process Classification framework. BPMI outperforms latent-space MI, max-uncertainty, and random baselines on both synthetic toy problems and a real-world laser-ignited rocket combustor, demonstrating faster convergence and more accurate probability maps. The approach includes an adaptive sampling frequency guided by aleatoric uncertainty, highlighting practical gains for resource allocation in complex multi-physics simulations with binary outcomes.

Abstract

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.

Figures (4)

• Figure 1: Bi-fidelity Gaussian Process classification model due to costabal2019multi used in this work. Variables on the left of the dashed line are hidden (latents), while $y_L$ and $y_H$ are the binary observed outcomes.
• Figure 2: Toy problems used in numerical experiments, showing the probability as a function of a 2D parameter space. Observed data at a given point is the outcome of Bernoulli trial using the probability at that point illustrated above.
• Figure 3: Comparison of active learning algorithms on the toy problems. BPMI consistently achieves higher ELPP and lower MSE than baseline methods across 20 independent runs.
• Figure 4: Application of proposed active learning method to a complex multi-physics solver. In (a) the ELPP over a held-out test set is shown. The random strategy is repeated three times, with the shaded region representing the standard deviation of these repeats. Due to computational limitations the BPMI strategy was only run once. Panels (b) to (e) show the points selected for simulations by each approach. Panels (f) to (i) show the predicted ignition probabilities of the final model for each fidelity under the two active learning algorithms compared here.