  Crystal structures are characterized by atomic bases within a primitive unit
cell that repeats along a regular lattice throughout 3D space. The periodic and
infinite nature of crystals poses unique challenges for geometric graph
representation learning. Specifically, constructing graphs that effectively
capture the complete geometric information of crystals and handle chiral
crystals remains an unsolved and challenging problem. In this paper, we
introduce a novel approach that utilizes the periodic patterns of unit cells to
establish the lattice-based representation for each atom, enabling efficient
and expressive graph representations of crystals. Furthermore, we propose
ComFormer, a SE(3) transformer designed specifically for crystalline materials.
ComFormer includes two variants; namely, iComFormer that employs invariant
geometric descriptors of Euclidean distances and angles, and eComFormer that
utilizes equivariant vector representations. Experimental results demonstrate
the state-of-the-art predictive accuracy of ComFormer variants on various tasks
across three widely-used crystal benchmarks. Our code is publicly available as
part of the AIRS library (https://github.com/divelab/AIRS).
