Efficient and Principled Scientific Discovery through Bayesian Optimization: A Tutorial

arXiv cs.LG / 4/3/2026

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Key Points

The tutorial argues that scientific discovery can be made more efficient by formalizing the hypothesis–experiment–refine loop as an optimization problem rather than an ad-hoc trial-and-error process.
It explains Bayesian Optimization (BO) as a probability-driven framework that uses surrogate models (such as Gaussian processes) to model evolving beliefs about unknown experimental outcomes.
BO’s acquisition functions are presented as the mechanism for selecting the next experiments by balancing exploitation (refining what’s already promising) with exploration (probing uncertain regions) to reduce wasted resources.
The article provides an end-to-end workflow and demonstrates practical effectiveness through case studies spanning catalysis, materials science, organic synthesis, and molecule discovery.
It also covers advanced BO extensions for real lab settings, including batched experimentation, heteroscedasticity handling, contextual optimization, and human-in-the-loop integration.

Abstract

Traditional scientific discovery relies on an iterative hypothesise-experiment-refine cycle that has driven progress for centuries, but its intuitive, ad-hoc implementation often wastes resources, yields inefficient designs, and misses critical insights. This tutorial presents Bayesian Optimisation (BO), a principled probability-driven framework that formalises and automates this core scientific cycle. BO uses surrogate models (e.g., Gaussian processes) to model empirical observations as evolving hypotheses, and acquisition functions to guide experiment selection, balancing exploitation of known knowledge and exploration of uncharted domains to eliminate guesswork and manual trial-and-error. We first frame scientific discovery as an optimisation problem, then unpack BO's core components, end-to-end workflows, and real-world efficacy via case studies in catalysis, materials science, organic synthesis, and molecule discovery. We also cover critical technical extensions for scientific applications, including batched experimentation, heteroscedasticity, contextual optimisation, and human-in-the-loop integration. Tailored for a broad audience, this tutorial bridges AI advances in BO with practical natural science applications, offering tiered content to empower cross-disciplinary researchers to design more efficient experiments and accelerate principled scientific discovery.