Barycentric Kernel for Bayesian Optimization of Chemical Mixture

Abstract

Chemical-reaction optimization not only increases the yield of chemical processes but also reduces impurities and improves the performance of the resulting products, contributing to important innovations in various industries. This paper presents a novel barycentric kernel for chemical-reaction optimization using Bayesian optimization (BO), a powerful machine-learning method designed to optimize costly black-box functions. The barycentric kernel is specifically tailored as a positive definite kernel for Gaussian-process surrogate models in BO, ensuring stability in logarithmic and differential operations while effectively mapping concentration space for solving optimization problems. We conducted comprehensive experiments comparing the proposed barycentric kernel with other widely used kernels, such as the radial basis function (RBF) kernel, across six benchmark functions in concentration space and three Hartmann functions in Euclidean space. The results demonstrated the barycentric kernel's stable convergence and superior performance in these optimization scenarios. Furthermore, the paper highlights the importance of accurately parameterizing chemical concentrations to prevent BO from searching for infeasible solutions. Initially designed for chemical reactions, the versatile barycentric kernel shows promising potential for a wide range of optimization problems, including those requiring a meaningful distance metric between mixtures.