Explicitly Incorporating Prior Knowledge into Bayesian Optimization for Materials Design

We propose a novel Bayesian optimization (BO) method that leverages researchers' knowledge of a linear relationship between experimental conditions x and a target property y to identify the optimal x with the fewest experiments. Knowledge is incorporated as the mean function μ-(x) of Gaussian process regression, and μ-(x) takes the form of a multivariate polynomial function of x, with appropriate prior distributions on the coefficients. These coefficients have prior distributions that reflect vague knowledge about the relationship between x and y, including the signs of the linear relationship. The posterior distribution of the coefficients is then obtained, and the acquisition functions in BO are derived using Markov chain Monte Carlo sampling to determine the next-to-be-tested x in the BO cycle. Through rigorous retrospective validations using mathematical simulation functions, a boiling-point data set, and a pigment data set, the method's utility and limitations were revealed. Compared with previously proposed BO approaches, the proposed method identified better solutions with fewer experimental trials when prior knowledge aligned with the underlying relationship between x and y.