  We propose an approach for exploiting machine learning to approximate
electronic fields in crystalline solids subjected to deformation. Strain
engineering is emerging as a widely used method for tuning the properties of
materials, and this requires repeated density functional theory calculations of
the unit cell subjected to strain. Repeated unit cell calculations are also
required for multi-resolution studies of defects in crystalline solids. We
propose an approach that uses data from such calculations to train a carefully
architected machine learning approximation. We demonstrate the approach on
magnesium, a promising light-weight structural material: we show that we can
predict the energy and electronic fields to the level of chemical accuracy, and
even capture lattice instabilities.
