Discovering phases and phase transitions using machine learning

Abstract

Machine learning a specific subset of artificial intelligence, trains a machine to learn from data. It has become a robust method for the identification of patterns within complex physical systems to determine certain physical quantities without prior knowledge of their physics principles. In this thesis work, we apply an unsupervised machine learning technique, Principal Component Analysis, and a supervised learning technique, Artificial Neural Networks, to identify phases and phase transitions in square and hexagonal lattice Ising models. It can be drawn from the results that Principal Component Analysis can successfully identify phase transitions and locate the transition temperatures in both square and hexagonal lattice systems. Additionally, it was found that two principal components are related to the order parameter and the susceptibility of the systems. The weight vectors have, then, a physical explanation, which is helpful to better understand system behavior. On the other hand, by employing neural networks, it was possible to understand the training effects of the Ising model, as well as obtain a critical temperature value ??C close to the real thermodynamic value. This confirms machine learning is suitable for approaching the type of complex systems studied in this research. Principal Component Analysis and neural network can learn from complex data, without the need of significant human intervention.