Accelerating Material Property Prediction using Generically Complete
  Isometry Invariants
Jonathan Balasingham Viktor Zamaraev Vitaliy Kurlin
Material or crystal property prediction using machine learning has grown
popular in recent years as it provides a computationally efficient replacement
to 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. While the PDD is
effective in distinguishing periodic point sets up to isometry, there is no
consideration for the composition of the underlying material. We develop a
transformer model with a modified self-attention mechanism that can utilize the
PDD and incorporate 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.