Machine Learning Modeling of Materials with a Group-Subgroup Structure

Crystal structures connected by continuous phase transitions are related through mathematical relationships 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 ML cost to reach 2-3 % target accuracy compared to conventional ML and Delta-ML. 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 only when the descriptor encodes structural information. The proposed approach is generic and extendable to other symmetry abstractions such as spin-, valency-, or charge order.