Exploring Machine Learning Techniques for Identifying Topological Transitions in Two-Dimensional Vortex Systems: A Study in Superconductors

Abstract

Abstract The advancement of Machine Learning (ML) is uprising and has seen significant uptick in the recent years. Therefore, this study will shed light on the two-dimensional vortex systems and the impact of ML on it. For the study—a rectangular, superconductor (Type II) system has been selected—the focus is to understand the topological transition, commonly known as melting, with a particular emphasis on leveraging ML techniques for its identification. To amplify this study, prior studies in the field are deeply examined, providing a detailed understanding. For instance, the Ginzburg–Landau theory serves as an important theoretical framework, showcasing the simulations used in this study. Brief descriptions are presented for the properties of the simulated material and the reason behind its selection, elaborating the research context. Subsequently, the simulated data undergoes pre-processing using Principal Component Analysis (PCA) as a preparatory step. This processed data is then utilized to train a logistic regression algorithm—referred as a simple yet effective classifier in this context. The resultant model shows success in accurately identifying the melting transition, presenting the efficacy of the employed approach. Despite the PCA and logistic regression simplicity compared to more complex ML algorithms; their effectiveness in this context is highly promising.