Bayesian optimization of atomic structures with prior probabilities from universal interatomic potentials

TL;DR

This study proposes a novel approach that combines the strengths of universal machine learning potentials with a Bayesian approach using Gaussian processes and turns out to improve the speed by which the global optimal structure is identified across diverse systems for a well-behaved machine learning potential.

Abstract

The optimization of atomic structures plays a pivotal role in understanding and designing materials with desired properties. However, conventional computational methods often struggle with the formidable task of navigating the vast potential energy surface, especially in high-dimensional spaces with numerous local minima. Recent advancements in machine learning-driven surrogate models offer a promising avenue for alleviating this computational burden. In this study, we propose a novel approach that combines the strengths of universal machine learning potentials with a Bayesian approach using Gaussian processes. By using the machine learning potentials as priors for the Gaussian process, the Gaussian process has to learn only the difference between the machine learning potential and the target energy surface calculated for example by density functional theory. This turns out to improve the speed by which the global optimal structure is identified across diverse systems for a well-behaved machine learning potential. The approach is tested on periodic bulk materials, surface structures, and a cluster.

Figures (6)

• Figure 1: Illustration of the GOFEE/BEACON cycle. The model starts with an initial training set of a few random structures, which are evaluated with DFT and included in a database on which a Gaussian process surrogate model is trained. The surrogate model is subsequently explored by minimizing the energy of a set of randomly picked initial structures. The obtained minima points on the surrogate surface are evaluated by means of an acquisition function, and the structure with the lowest value is selected. The energy and forces of this structure is calculated with DFT and the results are added to the database. The total number of cycles is set by the user.
• Figure 2: Left: Bulk SiO$_2$ success curve showing the cumulative success of finding the global minimum for each of the three priors. Shaded regions indicate the uncertainty based on Bayesian estimates (see Appendix).
• Figure 3: Left: Success curve for Cu$_{20}$ cluster. Right: Histogram of all DFT energies obtained during the runs.
• Figure 4: Progress of a single Cu$_{20}$BEACON run showing the predicted, DFT-calculated, and prior-predicted energies for each step. The green shaded area shows the uncertainty as estimated by the Gaussian process. Top: using the MACE-MP-0 prior. Bottom: using the standard mean prior. The initial structures are not included in the plot.
• Figure 5: Left: Success curve for anatase TiO$_2$(001)-(1 × 4) surface reconstruction. Right: Histogram of all DFT energies obtained during the runs.