Machine Learning Modeling of Materials with a Group-Subgroup Structure

TL;DR

This paper introduces group-subgroup machine learning (GS-ML) for materials with crystal structures, demonstrating improved prediction accuracy and efficiency by leveraging symmetry relations and a new dataset of organometallic materials.

Contribution

The study presents GS-ML, a novel approach incorporating crystallographic group-subgroup relations into machine learning models for materials prediction.

Findings

GS-ML reduces prediction errors for large unit cell materials.

GS-ML reaches 2-3% accuracy with minimal training cost.

The FriezeRMQ1D dataset contains 8393 materials across 7 frieze groups.

Abstract

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 7 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.