Bayesian optimization for materials design

TL;DR

This paper presents Bayesian optimization as an efficient method for materials design, leveraging Gaussian process regression to guide experiments and discover optimal materials with fewer trials.

Contribution

It introduces Bayesian optimization techniques tailored for materials design, including expected improvement and knowledge-gradient methods, with detailed derivations and theoretical properties.

Findings

Bayesian optimization effectively guides materials experiments.

Expected improvement and knowledge-gradient methods are derived and analyzed.

The methods achieve one-step Bayes-optimality in design problems.

Abstract

We introduce Bayesian optimization, a technique developed for optimizing time-consuming engineering simulations and for fitting machine learning models on large datasets. Bayesian optimization guides the choice of experiments during materials design and discovery to find good material designs in as few experiments as possible. We focus on the case when materials designs are parameterized by a low-dimensional vector. Bayesian optimization is built on a statistical technique called Gaussian process regression, which allows predicting the performance of a new design based on previously tested designs. After providing a detailed introduction to Gaussian process regression, we introduce two Bayesian optimization methods: expected improvement, for design problems with noise-free evaluations; and the knowledge-gradient method, which generalizes expected improvement and may be used in design problems with noisy evaluations. Both methods are derived using a value-of-information analysis, and enjoy one-step Bayes-optimality.