Crystal structures connected by continuous phase transitions are linked through mathematical relations between crystallographic groups and their subgroups. In the present study, we introduce group-subgroup machine learning (GS-ML) and show that including materials with small unit cells in the training set decreases out-of-sample prediction errors for materials with large unit cells. GS-ML incurs the least training cost to reach 2%–3% target accuracy compared to other ML approaches. Since available materials datasets are heterogeneous providing insufficient examples for realizing the group-subgroup structure, we present the ‘FriezeRMQ1D’ dataset with 8393 Q1D organometallic materials uniformly distributed across seven frieze groups. Furthermore, by comparing the performances of FCHL and 1-hot representations, we show GS-ML to capture subgroup information efficiently when the descriptor encodes structural information. The proposed approach is generic and extendable to symmetry abstractions such as spin-, valency-, or charge order.

通过连续相变连接的晶体结构通过晶体群及其子群之间的数学关系联系起来。在本研究中，我们介绍了组-子组机器学习(GS-ML) 并表明在训练集中包含具有小晶胞的材料可降低具有大晶胞的材料的样本外预测误差。与其他 ML 方法相比，GS-ML 达到 2%–3% 的目标准确率所需的训练成本最低。由于可用的材料数据集是异构的，无法为实现组-子组结构提供足够的示例，因此我们提出了“FriezeRMQ1D”数据集，其中包含 8393 个 Q1D 有机金属材料，均匀分布在七个楣组中。此外，通过比较 FCHL 和 1-hot 表示的性能，我们展示了当描述符对结构信息进行编码时，GS-ML 可以有效地捕获子组信息。所提出的方法是通用的，可扩展到对称抽象，如自旋、价或电荷顺序。