Machine Learning for Identifying Dynamical Phases in Topological Lasers

Identifying phases and analyzing the stability of dynamic states are common and important problems that appear in a variety of physical systems. However, drawing a phase diagram in high-dimensional and large parameter spaces has proven to be challenging. In this chapter, we will look at a data-driven method to obtain the phase diagram of lasing modes in photonic topological insulator lasers. The classification is based on the temporal behaviour of the topological modes obtained via numerical integration of the rate equation. An unsupervised learning method is used and an adaptive library is constructed in order to distinguish the different topological modes present in the generated parameter space. We start by introducing photonic topological lasers and Su-Schrieffer-Heeger lattices with saturable gain. Then, we look at different dynamic mode decomposition methods for a parameter space defined as the gain and loss parameters. Finally, we classify the topological phases of the topological lasing modes using the library automatically determined by top-down and bottom-up classification approaches.