Zikai Xie

Zikai Xie, Xenophon Evangelopoulos, Joseph Thacker et al.

In this paper we propose DKIBO, a Bayesian optimization (BO) algorithm that accommodates domain knowledge to tune exploration in the search space. Bayesian optimization has recently emerged as a sample-efficient optimizer for many intractable scientific problems. While various existing BO frameworks allow the input of prior beliefs to accelerate the search by narrowing down the space, incorporating such knowledge is not always straightforward and can often introduce bias and lead to poor performance. Here we propose a simple approach to incorporate structural knowledge in the acquisition function by utilizing an additional deterministic surrogate model to enrich the approximation power of the Gaussian process. This is suitably chosen according to structural information of the problem at hand and acts a corrective term towards a better-informed sampling. We empirically demonstrate the practical utility of the proposed method by successfully injecting domain knowledge in a materials design task. We further validate our method's performance on different experimental settings and ablation analyses.

Zhongwei Yu, Rasul Tutunov, Alexandre Max Maraval et al.

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.

Zikai Xie, Linjiang Chen

Bayesian Optimization (BO) is a powerful tool for black-box optimization, but its application to high-dimensional permutation spaces is severely limited by the challenge of defining scalable representations. The current state-of-the-art BO approach for permutation spaces relies on an exhaustive $Ω(n^2)$ pairwise comparison, inducing a dense representation that is impractical for large-scale permutations. To break this barrier, we introduce a novel framework for generating efficient permutation representations via kernel functions derived from sorting algorithms. Within this framework, the Mallows kernel can be viewed as a special instance derived from enumeration sort. Further, we introduce the \textbf{Merge Kernel} , which leverages the divide-and-conquer structure of merge sort to produce a compact, $Θ(n\log n)$ to achieve the lowest possible complexity with no information loss and effectively capture permutation structure. Our central thesis is that the Merge Kernel performs competitively with the Mallows kernel in low-dimensional settings, but significantly outperforms it in both optimization performance and computational efficiency as the dimension $n$ grows. Extensive evaluations on various permutation optimization benchmarks confirm our hypothesis, demonstrating that the Merge Kernel provides a scalable and more effective solution for Bayesian optimization in high-dimensional permutation spaces, thereby unlocking the potential for tackling previously intractable problems such as large-scale feature ordering and combinatorial neural architecture search.