Machine learning of octahedral tilting in oxide perovskites by symbolic classification with compressed sensing

The steady growth of online materials databases, coupled with efforts in materials informatics, has invited the reexamination of existing empirical models through the lens of modern machine learning techniques. Inspired by recent efforts to improve on the Goldschmidt tolerance factor for perovskite formation, we apply the symbolic regression to the problem of predicting octahedral tilting. In addition to its impact on the crystal structure, octahedral tilting is related to functional properties, including dielectric permittivity, ferroelectricity, magnetic properties, and metal–insulator transitions. By relating a selection of physical parameters (e.g., atomic radii, electronegativity) with mathematical operations (e.g., addition, exponentiation), we identify an analytical equation that correctly predicts the octahedral tilting classification for 49 perovskite oxides in a dataset of 60 materials. Using the same training dataset, we additionally fit and compare seven models generated by other common machine learning methods. Despite the increased complexity afforded by support vector machines, decision trees/random forests, and artificial neural networks, we find that our equation outperforms the other models as well as the original tolerance factor in predicting octahedral tilting.