  Grain boundaries dramatically affect the properties of polycrystalline
materials because of differences in atomic configuration. To fully understand
the relationship between grain boundaries and materials properties, systematic
studies of the grain boundary atomic structure are crucial. However, such
studies are limited by the extensive computation necessary to determine the
structure of a single grain boundary. If the structure could be predicted with
more efficient computation, the understanding of the grain boundary would be
accelerated significantly. Here, we predict grain boundary structures and
energies using a machine-learning technique. Training data for non-linear
regression of four symmetric-tilt grain boundaries of copper were used. The
results of the regression analysis were used to predict 12 other grain boundary
structures. The method accurately predicts both the structures and energies of
grain boundaries. The method presented in this study is very general and can be
utilized in understanding many complex interfaces.
