Crystal Hypergraph Convolutional Networks

Modern machine learning models for materials science applications generally employ the use of graph neural networks (GNNs). Such constructions restrict representations to atom and pair-wise descriptions or features that are updated via messages composed of origin and neighboring atom features, as well as the corresponding 'bond' features. In this talk, we propose a natural extension of such frameworks, which employs the use of hypergraphs to generalize to higher-order geometrical structures (such as triplets and motifs) within the same mathematical representation of the crystal. In the framework of crystal hypergraphs, we propose two new convolutional functions applicable to these higher-order edges (that is, hyperedges containing more than two nodes): one that converts a hypergraph to a corresponding graph (upon which the usual techniques of graph convolution apply); and another that aggregates node features contained in each hyperedge to form a 'neighborhood' feature for use in update messages. Both approaches proposed here thus relax the restriction of representations of materials systems to atom and pair-wise descriptions, allowing us to naturally encode higher-order geometrical structures of such systems, while maintaining the permutation and coordinate-system invariant properties of graph neural networks. The proposed crystal hypergraph convolutional network will serve as a general framework to incorporate multi-tier material information in machine learning of crystals and beyond.