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

TL;DR

This paper introduces a data-driven, semi-supervised machine learning method to classify topological lasing modes in complex parameter spaces, enabling phase diagram construction without expert knowledge.

Contribution

The paper presents a novel semi-supervised learning approach to identify topological phases in laser systems, reducing reliance on expert input and facilitating phase diagram analysis.

Findings

Successfully classifies topological phases in SSH lattice with saturable gain.

Demonstrates the method's ability to distinguish phases in high-dimensional parameter spaces.

Provides a new tool for analyzing the physics of topological insulator lasers.

Abstract

Identifying phases and analyzing the stability of dynamic states are ubiquitous and important problems which appear in various physical systems. Nonetheless, drawing a phase diagram in high-dimensional and large parameter spaces has remained challenging. Here, we propose a data-driven method to derive the phase diagram of lasing modes in topological insulator lasers. The classification is based on the temporal behaviour of the topological modes obtained via numerical integration of the rate equation. A semi-supervised learning method is used and an adaptive library is constructed in order to distinguish the different topological modes present in the generated parameter space. The proposed method successfully distinguishes the different topological phases in the Su-Schrieffer-Heeger (SSH) lattice with saturable gain.This demonstrates the possibility of classifying the topological phases without needing for expert knowledge of the system and may give valuable insight into the fundamental physics of topological insulator lasers via reverse engineering.