Topological data analysis assisted machine learning for polar topological structures in oxide superlattices

Ferroelectric topological phases and phase transitions have been extensively investigated recently due to the rich physical insights and potential applications in next-generation electronic devices. However, precisely predicting the topological phase transitions under different internal and external conditions in polar oxide superlattice systems is challenging due to the complex energy competitions and highly nonlinear kinetics involved. Herein, we adopted a state-of-the-art mathematical concept called "persistent homology" from topological data analysis to extract the essential topological features for the polarization data in various topological structures. By implementing the persistent image as the descriptor, support vector regression (SVR) based convolutional neural network (CNN) models are developed for the automated and high precision classification and regression of topological states based on high-dimensional phase-field simulation data of the PTO/STO superlattice. Using this method, we can automatically construct the strain and electric field phase diagrams in seconds with high throughput phase-field data. We hope to spur further interest in the integration of state-of-the-art mathematical tools, machine learning algorithms, and condensed matter physics for predictions of topological phase transitions.