  Periodic material or crystal property prediction using machine learning has
grown popular in recent years as it provides a computationally efficient
replacement for classical simulation methods. A crucial first step for any of
these algorithms is the representation used for a periodic crystal. While
similar objects like molecules and proteins have a finite number of atoms and
their representation can be built based upon a finite point cloud
interpretation, periodic crystals are unbounded in size, making their
representation more challenging. In the present work, we adapt the Pointwise
Distance Distribution (PDD), a continuous and generically complete isometry
invariant for periodic point sets, as a representation for our learning
algorithm. The PDD distinguished all (more than 660 thousand) periodic crystals
in the Cambridge Structural Database as purely periodic sets of points without
atomic types. We develop a transformer model with a modified self-attention
mechanism that combines PDD with compositional information via a spatial
encoding method. This model is tested on the crystals of the Materials Project
and Jarvis-DFT databases and shown to produce accuracy on par with
state-of-the-art methods while being several times faster in both training and
prediction time.
