Gaussian process regression acceleration of calculations for determining the mechanism and rate of atomic rearrangements

Calculations of minimum energy paths and searches for saddle points on energy surfaces to characterize the mechanism of atomic rearrangements and estimate their rate can be accelerated using machine learning based on Gaussian process regresssion by reducing the number of energy and atomic force evaluations needed to reach convergence. While standard squared exponential covariance function can give good performance in some cases [1], problems can arise when configurations with large forces due to short distance between atoms are included in the data set. A greatly improved performance is obtained by using a non-stationary covariance function based on inverse distances between pairs of atoms [2]. Calculations using the nudged elastic band method for finding minimum energy paths and minimum mode following method for finding first order saddle points [3] are presented for various chemical reactions and structural transitions on solid surfaces. The use of Gaussian process regression can reduce the number of energy and force evaluations by an order of magnitude.