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 to enable batch-wise optimization on both direct and latent crystallographic representations. Using the GPU acceleration, this 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 escape local minima defined by different objective gradients, thus increasing the success rate of generating complex structures satisfying the target 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.

翻译：本文提出了一种材料生成框架，该框架将对称性条件变分自编码器（CVAE）与可微分的SO(3)功率谱目标函数相结合，以在晶体学约束下引导候选结构朝向指定的局域环境。具体而言，我们实现了一个全可微分流程，从而能够在直接晶体学表示和潜在晶体学表示上进行批量优化。利用GPU加速，该实现相比我们之前的CPU工作流程实现了约五倍的速度提升，同时获得了可比较的结果。此外，我们引入了一种交替在直接晶体表示和潜在晶体表示上进行优化的策略。这种双级弛豫方法能够有效逃离由不同目标梯度定义的局部极小值，从而提高了生成满足目标局域环境的复杂结构的成功率。该框架可扩展至由多组分和多环境构成的系统，为生成具有目标局域环境的材料结构提供了一条可扩展的途径。