  We consider the problem of generating periodic materials with deep models.
While symmetry-aware molecule generation has been studied extensively, periodic
materials possess different symmetries, which have not been completely captured
by existing methods. In this work, we propose SyMat, a novel material
generation approach that can capture physical symmetries of periodic material
structures. SyMat generates atom types and lattices of materials through
generating atom type sets, lattice lengths and lattice angles with a
variational auto-encoder model. In addition, SyMat employs a score-based
diffusion model to generate atom coordinates of materials, in which a novel
symmetry-aware probabilistic model is used in the coordinate diffusion process.
We show that SyMat is theoretically invariant to all symmetry transformations
on materials and demonstrate that SyMat achieves promising performance on
random generation and property optimization tasks. Our code is publicly
available as part of the AIRS library (https://github.com/divelab/AIRS).
