用傅里叶变换表示晶体，实现高效生成与对称性建模
Fourier Transformers for Latent Crystallographic Diffusion and Generative Modeling
- 以傅里叶系数替代原子坐标，天然满足周期性和对称性
- 仅用每维9个基函数即可重建含108原子/物种的晶胞
- 适合需要高对称性约束的大规模晶体生成任务
新晶体材料的发现需要能处理周期边界、晶格对称性和物理约束的生成模型，同时支持大而结构多样的原胞。我们提出一种倒空间生成流程，通过物种分辨原胞密度的截断傅里叶变换来表示晶体，而非直接建模原子坐标。该表示天然具备周期性，可简单代数实现空间群对称操作，并在生成中自然支持可变原子多重性，克服了粒子基方法的常见局限。仅使用每空间维度9个傅里叶基函数，本方法可重构每化学物种最多108个原子的原胞。我们基于复值傅里叶系数构建了变压器变分自编码器和潜在扩散模型，在LeMaterial基准上评估了重建性能与潜在扩散效果，并在小原胞情形（≤16原子/原胞）下与基于坐标的基线方法进行了无条件生成对比。
原文摘要 · Abstract (English)
The discovery of new crystalline materials calls for generative models that handle periodic boundary conditions, crystallographic symmetries, and physical constraints, while scaling to large and structurally diverse unit cells. We propose a reciprocal-space generative pipeline that represents crystals through a truncated Fourier transform of the species-resolved unit-cell density, rather than modeling atomic coordinates directly. This representation is periodicity-native, admits simple algebraic actions of space-group symmetries, and naturally supports variable atomic multiplicities during generation, addressing a common limitation of particle-based approaches. Using only nine Fourier basis functions per spatial dimension, our approach reconstructs unit cells containing up to 108 atoms per chemical species. We instantiate this pipeline with a transformer variational autoencoder over complex-valued Fourier coefficients, and a latent diffusion model that generates in the compressed latent space. We evaluate reconstruction and latent diffusion on the LeMaterial benchmark and compare unconditional generation against coordinate-based baselines in the small-cell regime ($\leq 16$ atoms per unit cell).
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