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Identifying phases and analyzing the stability of dynamic states areubiquitous and important problems which appear in various physical systems.Nonetheless, drawing a phase diagram in high-dimensional and large parameterspaces has remained challenging. Here, we propose a data-driven method toderive the phase diagram of lasing modes in topological insulator lasers. Theclassification is based on the temporal behaviour of the topological modesobtained via numerical integration of the rate equation. A semi-supervisedlearning method is used and an adaptive library is constructed in order todistinguish the different topological modes present in the generated parameterspace. The proposed method successfully distinguishes the different topologicalphases in the Su-Schrieffer-Heeger (SSH) lattice with saturable gain.Thisdemonstrates the possibility of classifying the topological phases withoutneeding for expert knowledge of the system and may give valuable insight intothe fundamental physics of topological insulator lasers via reverseengineering.

A machine learning approach to drawing phase diagrams of topological lasing modes