Material Property Prediction using Graphs based on Generically Complete Isometry Invariants

The structure-property hypothesis says that the properties of all materials are determined by an underlying crystal structure. The main obstacle was the ambiguity of conventional crystal representations based on incomplete or discontinuous descriptors that allow false negatives or false positives. This ambiguity was resolved by the ultra-fast Pointwise Distance Distribution (PDD), which distinguished all periodic structures in the world's largest collection of real materials (Cambridge Structural Database). The state-of-the-art results in property predictions were previously achieved by graph neural networks based on various graph representations of periodic crystals, including the Crystal Graph with vertices at all atoms in a crystal unit cell. This work adapts the Pointwise Distance Distribution for a simpler graph whose vertex set is not larger than the asymmetric unit of a crystal structure. The new Distribution Graph reduces mean-absolute-error by 0.6%-12% while having 44%-88% of the number of vertices when compared to the crystal graph when applied on the Materials Project and Jarvis-DFT datasets using CGCNN and ALIGNN. Methods for hyper-parameters selection for the graph are backed by the theoretical results of the Pointwise Distance Distribution and are then experimentally justified.