  Generative design marks a significant data-driven advancement in the
exploration of novel inorganic materials, which entails learning the symmetry
equivalent to the crystal structure prediction (CSP) task and subsequent
learning of their target properties. Generative models have been developed in
the last few years that use custom Variational Autoencoders (VAEs), Generative
Adversarial Networks (GANs), and diffusion models. While periodicity and global
Euclidian symmetry in three dimensions through translations, rotations and
reflections have recently been accounted for, symmetry constraints within
allowed space groups have not. This is especially important because the final
step involves energy relaxation on the generated crystal structures to find the
relaxed crystal structure, typically using Density Functional Theory (DFT). To
address this explicitly, we introduce a generative design framework (WyCryst),
composed of three pivotal components: 1) a Wyckoff position based inorganic
crystal representation, 2) a property-directed VAE model and 3) an automated
DFT workflow for structure refinement. Our model selectively generates
materials that follow the ground truth of unit cell space group symmetry by
encoding the Wyckoff representation for each space group. We successfully
reproduce a variety of existing materials: CaTiO3 (space group, SG No. 62 and
221), CsPbI3 (SG No. 221), BaTiO3 (SG No. 160), and CuInS2 (SG No.122) for both
ground state as well as polymorphic structure predictions. We also generate
several new ternary materials not found in the inorganic materials database
(Materials Project), which are proved to be stable, retaining their symmetry,
and we also check their phonon stability, using our automated DFT workflow
highlighting the validity of our approach. We believe our symmetry-aware
WyCryst takes a vital step towards AI-driven inorganic materials discovery.
