Crystal Generation using the Fully Differentiable Pipeline and Latent Space Optimization

We present a materials generation framework that couples a symmetry-conditioned variational autoencoder (CVAE) with a differentiable SO(3) power spectrum objective to steer candidates toward a specified local environment under the crystallographic constraints. In particular, we implement a fully differentiable pipeline that performs batch-wise optimization on both direct and latent crystallographic representations. Using the GPU acceleration, the implementation achieves about fivefold speed compared to our previous CPU workflow, while yielding comparable outcomes. In addition, we introduce the optimization strategy that alternatively performs optimization on the direct and latent crystal representations. This dual-level relaxation approach can effectively overcome local barrier defined by different objective gradients, thus increasing the success rate of generating complex structures satisfying the targe local environments. This framework can be extended to systems consisting of multi-components and multi-environments, providing a scalable route to generate material structures with the target local environment.