Benchmarking the performance of Bayesian optimization across multiple experimental materials science domains

Bayesian optimization (BO) has been leveraged for guiding autonomous and high-throughput experiments in materials science. However, few have evaluated the efficiency of BO across a broad range of experimental materials domains. In this work, we quantify the performance of BO with a collection of surrogate model and acquisition function pairs across five diverse experimental materials systems. By defining acceleration and enhancement metrics for materials optimization objectives, we find that surrogate models such as Gaussian Process (GP) with anisotropic kernels and Random Forest (RF) have comparable performance in BO, and both outperform the commonly used GP with isotropic kernels. GP with anisotropic kernels has demonstrated the most robustness, yet RF is a close alternative and warrants more consideration because it is free from distribution assumptions, has smaller time complexity, and requires less effort in initial hyperparameter selection. We also raise awareness about the benefits of using GP with anisotropic kernels in future materials optimization campaigns.

Two-sample statistics based on anisotropic kernels

The paper introduces a new kernel-based Maximum Mean Discrepancy (MMD) statistic for measuring the distance between two distributions given finitely many multivariate samples. When the distributions are locally low-dimensional, the proposed test can be made more powerful to distinguish certain alternatives by incorporating local covariance matrices and constructing an anisotropic kernel. The kernel matrix is asymmetric; it computes the affinity between $n$ data points and a set of $n_R$ reference points, where $n_R$ can be drastically smaller than $n$. While the proposed statistic can be viewed as a special class of Reproducing Kernel Hilbert Space MMD, the consistency of the test is proved, under mild assumptions of the kernel, as long as $\|p-q\| \sqrt{n} \to \infty $, and a finite-sample lower bound of the testing power is obtained. Applications to flow cytometry and diffusion MRI datasets are demonstrated, which motivate the proposed approach to compare distributions.

The Space–Time Kernel-Based Numerical Method for Burgers’ Equations

It is well known that major error occur in the time integration instead of the spatial approximation. In this work, anisotropic kernels are used for temporal as well as spatial approximation to construct a numerical scheme for solving nonlinear Burgers’ equations. The time-dependent PDEs are collocated in both space and time first, contrary to spatial discretization, and time stepping procedures for time integration are then applied. Physically one cannot in general expect that the spatial and temporal features of the solution behaves on the same order. Hence, one should have to incorporate anisotropic kernels. The nonlinear Burgers’ equations are converted by nonlinear transformation to linear equations. The spatial discretizations are carried out to construct differentiation matrices. Comparisons with most available numerical methods are made to solve the Burgers’ equations.