Machine learning modeling of materials with a group-subgroup structure

Abstract

A cornerstone of materials science is Landau’s theory of continuous phase transitions. Crystal structures connected by Landau-type transitions are mathematically related through groupsubgroup relationships. In this study, we introduce “group-subgroup learning” and show including small unit cell phases of materials in the training set to decrease out-of-sample errors for modeling larger phases. The proposed approach is generic and is independent of the ML formalism, descriptors, or datasets; and extendable to other symmetry abstractions such as spin-, valency-, or charge order. Since available materials datasets are heterogeneous with too few examples for realizing the group-subgroup structure, we present the “FriezeRMQ1D” dataset of 8393 Q1D organometallic materials uniformly distributed across seven frieze groups and provide a proof-of-the-concept. For these materials, we report < 3% error with 25% training with the Faber–Christensen–Huang–Lilienfeld descriptor and compare its performance with a fingerprint representation that encodes materials composition as well as crystallographic Wyckoff positions.