Machine Learning Based Prediction of Polaron-Vacancy Patterns on the TiO$_2$(110) Surface

The multifaceted physics of oxides is shaped by their composition and the presence of defects, which are often accompanied by the formation of polarons. The simultaneous presence of polarons and defects, and their complex interactions, pose challenges for first-principles simulations and experimental techniques. In this study, we leverage machine learning and a first-principles database to analyze the distribution of surface oxygen vacancies (V$_{\rm O}$) and induced small polarons on rutile TiO$_2$(110), effectively disentangling the interactions between polarons and defects. By combining neural-network supervised learning and simulated annealing, we elucidate the inhomogeneous V$_{\rm O}$ distribution observed in scanning probe microscopy (SPM). Our innovative approach allows us to understand and predict defective surface patterns at previously inaccessible length scales, identifying the specific role of individual types of defects. Specifically, surface-polaron-stabilizing V$_{\rm O}$-configurations are identified, which could have consequences for surface reactivity.