Crystals are the foundation of numerous scientific and industrial applications. While various learning-based approaches have been proposed for crystal generation, existing methods seldom consider the space group constraint which is crucial in describing the geometry of crystals and closely relevant to many desirable properties. However, considering space group constraint is challenging owing to its diverse and nontrivial forms. In this paper, we reduce the space group constraint into an equivalent formulation that is more tractable to be handcrafted into the generation process. In particular, we translate the space group constraint into two parts: the basis constraint of the invariant logarithmic space of the lattice matrix and the Wyckoff position constraint of the fractional coordinates. Upon the derived constraints, we then propose DiffCSP++, a novel diffusion model that has enhanced a previous work DiffCSP by further taking space group constraint into account. Experiments on several popular datasets verify the benefit of the involvement of the space group constraint, and show that our DiffCSP++ achieves promising performance on crystal structure prediction, ab initio crystal generation and controllable generation with customized space groups.

翻译：晶体是众多科学与工业应用的基础。尽管已有多种基于学习的方法被提出用于晶体生成，现有方法很少考虑在描述晶体几何结构及与诸多理想性质密切相关的关键约束——空间群约束。然而，由于空间群形式多样且结构复杂，对其施加约束极具挑战性。本文提出将空间群约束转化为更易融入生成过程的等效表达式。具体而言，我们将空间群约束分解为两部分：晶格矩阵不变对数空间的基约束，以及分数坐标的Wyckoff位置约束。基于导出的约束条件，我们进一步提出DiffCSP++——一种在先前工作DiffCSP基础上引入空间群约束增强的新型扩散模型。在多个公开数据集上的实验证实了引入空间群约束的有效性，结果表明DiffCSP++在晶体结构预测、从头晶体生成以及自定义空间群的可控生成任务中均展现出优越性能。