Accelerating Material Property Prediction using Generically Complete Isometry Invariants

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.