Enhancing ab initio diffusion calculations in materials through Gaussian process regression

Abstract: Saddle point search schemes are widely used to identify the transition state of different processes, like chemical reactions, surface and bulk diffusion, surface adsorption, and many more. In solid-state materials with relatively large numbers of atoms, the minimum mode following schemes such as dimer are commonly used because they alleviate the calculation of the Hessian on the high-dimensional potential energy surface. Here, we show that the dimer search can be further accelerated by leveraging Gaussian process regression (GPR). The GPR serves as a surrogate model to feed the dimer with the required energy and force input. We test the GPR- accelerated dimer method for predicting the diffusion coefficient of vacancy-mediated self-diffusion in bcc molybdenum and sulfur diffusion in hexagonal molybdenum disulfide. We use a multi-task learning approach that utilizes a shared covariance function between energy and force input, and we show that the multi-task learning significantly improves the performance of the GPR surrogate model compared to previously used learning approaches. Additionally, we demonstrate that a translation-hop sampling approach is necessary to avoid over-fitting the GPR surrogate model to the minimum-mode-following pathway and thus succeeding in locating the saddle point. We show that our method reduces the number of evaluations to a fraction of what a conventional dimer requires.