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.

AI-Assisted Rapid Crystal Structure Generation Towards a Target Local Environment

In the field of material design, traditional crystal structure prediction approaches require extensive structural sampling through computationally expensive energy minimization methods using either force fields or quantum mechanical simulations. While emerging artificial intelligence (AI) generative models have shown great promise in generating realistic crystal structures more rapidly, most existing models fail to account for the unique symmetries and periodicity of crystalline materials, and they are limited to handling structures with only a few tens of atoms per unit cell. Here, we present a symmetry-informed AI generative approach called Local Environment Geometry-Oriented Crystal Generator (LEGO-xtal) that overcomes these limitations. Our method generates initial structures using AI models trained on an augmented small dataset, and then optimizes them using machine learning structure descriptors rather than traditional energy-based optimization. We demonstrate the effectiveness of LEGO-xtal by expanding from 25 known low-energy sp2 carbon allotropes to over 1,700, all within 0.5 eV/atom of the ground-state energy of graphite. This framework offers a generalizable strategy for the targeted design of materials with modular building blocks, such as metal-organic frameworks and next-generation battery materials.