  Crystal Structure Prediction (CSP) aims to discover solid crystalline
materials by optimizing periodic arrangements of atoms, ions or molecules. CSP
takes weeks of supercomputer time because of slow energy minimizations for
millions of simulated crystals. The lattice energy is a key physical property,
which determines thermodynamic stability of a crystal but has no simple
analytic expression. Past machine learning approaches to predict the lattice
energy used slow crystal descriptors depending on manually chosen parameters.
The new area of Periodic Geometry offers much faster isometry invariants that
are also continuous under perturbations of atoms. Our experiments on simulated
crystals confirm that a small distance between the new invariants guarantees a
small difference of energies. We compare several kernel methods for
invariant-based predictions of energy and achieve the mean absolute error of
less than 5kJ/mole or 0.05eV/atom on a dataset of 5679 crystals.
