Machine learning phases in swarming systems

Recent years have witnessed a growing interest in using machine learning to predict and identify phase transitions (PTs) in various systems. Here we adopt convolutional neural networks (CNNs) to study the PTs of Vicsek model, solving the problem that traditional order parameters are insufficiently able to do. Within the large-scale simulations, there are four phases, and we confirm that all the PTs between two neighboring phases are first-order. We have successfully classified the phase by using CNNs with a high accuracy and identified the PT points, while traditional approaches using various order parameters fail to obtain. These results indicate the great potential of machine learning approach in understanding the complexities in collective behaviors, and in related complex systems in general.