  The calculation of minimum energy paths for transitions such as atomic and/or
spin re-arrangements is an important task in many contexts and can often be
used to determine the mechanism and rate of transitions. An important challenge
is to reduce the computational effort in such calculations, especially when ab
initio or electron density functional calculations are used to evaluate the
energy since they can require large computational effort. Gaussian process
regression is used here to reduce significantly the number of energy
evaluations needed to find minimum energy paths of atomic rearrangements. By
using results of previous calculations to construct an approximate energy
surface and then converge to the minimum energy path on that surface in each
Gaussian process iteration, the number of energy evaluations is reduced
significantly as compared with regular nudged elastic band calculations. For a
test problem involving rearrangements of a heptamer island on a crystal
surface, the number of energy evaluations is reduced to less than a fifth. The
scaling of the computational effort with the number of degrees of freedom as
well as various possible further improvements to this approach are discussed.
