基于空间群对称性生成晶体结构，提升材料逆向设计效率。
Space Group Equivariant Crystal Diffusion
- 利用空间群不变的似然函数与等变扩散模型建模晶体对称性。
- 在标准数据集上性能超越现有方法，量子计算验证结果更优。
- 适合材料设计、生成模型研究者快速生成符合物理规律的晶体。
利用生成模型加速晶体材料的逆向设计具有广泛技术意义。不同于其他原子系统，三维晶体对离散等距变换群——空间群具有不变性，而这些对称性显著影响材料性质。我们提出 SGEquiDiff，一种能自然处理空间群约束的晶体生成模型，采用空间群不变的似然函数。该模型包含：基于 SE(3) 不变的晶格离散渐进采样器；基于变换器的原子位置、元素及对称唯一原子数的排列不变自回归采样；以及原子坐标的空间群等变扩散过程。我们证明空间群等变向量场自动位于威克夫位置的切空间中。SGEquiDiff 在标准基准数据集上通过定量代理指标和量子力学计算评估，达到当前最优性能。代码已开源：https://github.com/rees-c/sgequidiff。
原文摘要 · Abstract (English)
Accelerating inverse design of crystalline materials with generative models has significant implications for a range of technologies. Unlike other atomic systems, 3D crystals are invariant to discrete groups of isometries called the space groups. Crucially, these space group symmetries are known to heavily influence materials properties. We propose SGEquiDiff, a crystal generative model which naturally handles space group constraints with space group invariant likelihoods. SGEquiD-iff consists of an SE(3)-invariant, telescoping discrete sampler of crystal lattices; permutation-invariant, transformer-based autoregressive sampling of Wyckoff positions, elements, and numbers of symmetrically unique atoms; and space group equivariant diffusion of atomic coordinates. We show that space group equivariant vector fields automatically live in the tangent spaces of the Wyckoff positions. SGEquiDiff achieves state-of-the-art performance on standard benchmark datasets as assessed by quantitative proxy metrics and quantum mechanical calculations. Our code is available at https://github.com/rees-c/sgequidiff.
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