Enhancing ab initio diffusion calculations in materials through Gaussian process regression

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.