  The grain boundary (GB) energy has a profound influence on the grain growth
and properties of polycrystalline metals. Here, we show that the energy of a
GB, normalized by the bulk cohesive energy, can be described purely by four
geometric features. By machine learning on a large computed database of 361
small $\Sigma$ ($\Sigma < 10$) GBs of more than 50 metals, we develop a model
that can predict the grain boundary energies to within a mean absolute error of
0.13 J m$^{-2}$. More importantly, this universal GB energy model can be
extrapolated to the energies of high $\Sigma$ GBs without loss in accuracy.
These results highlight the importance of capturing fundamental scaling physics
and domain knowledge in the design of interpretable, extrapolatable machine
learning models for materials science.
