The materials data used to discover potential stable magnetic materials is generated by our CubicGAN , which is a crystal generative model that can generate crystal structures for three cubic space groups at a large scale. CubicGAN tackles the crystal generative design challenges one by one via: 1) Nonequivalent atom positions are used to represent atoms' arrangement in unit cell. We chose ternary materials that have only nonequivalent atom positions (a.k.a, one element has one nonequivalent atom positions). In this way, the size of input data to the generative model can be same if we train a generator to generate only ternary materials. To obtain all atom positions in the unit cell, affine matrix is used to convert nonequivalent atom positions. Affine matrix is determined by space groups and it contains rotation and translation matrices. 2) Only cubic ternary materials are used to grain the generator. In this way, we only need to generate the length of cubic lattice. The angles are all 90 • . Then we discretize fractional coordinates by using fractional coordinate values in the set of {0.0, 0.25, 0.5, 0.75}. 3) We are not trying to generate crystal structures in 230 space groups like what VAE models claim . Instead, VAE models always generate crystal structures with very low symmetry . On the other hand, we only use materials falling in three space groups of Fm 3m, F 43m, and Pm 3m because these three space groups are with greatest number of materials in OQMD using selection criteria in CubicGAN. The main framework of CubicGAN is illustrated in Figure . The framework primarily contains two learning parts: generator and discriminator. The generator takes elements, space groups, and random noise as input and then generate three non-equivalent fractional coordinates B f ake and lattice parameters P f ake (only lengths since cubic structures have constant angles). With random chosen space group S f ake and Elements E f ake , we can assemble M f ake = (B f ake , P f ake , S f ake , E f ake ) as the fake samples and the real samples M real = (B real , P real , S real , E real ) are collected through real crystal structures. Then discriminator learns to tell fake samples from real samples via two losses of L adv and L dis which are define below :