Unsupervised Learning of non-Hermitian Photonic Bulk Topology

Machine-learning has proven useful in distinguishing topological phases. However, there is still a lack of relevant research in the non-Hermitian community, especially from the perspective of the momentum-space. Here, an unsupervised machine-learning method, diffusion maps, is used to study non-Hermitian topologies in the momentum-space. Choosing proper topological descriptors as input datasets, topological phases are successfully distinguished in several prototypical cases, including a line-gapped tight-binding model, a line-gapped Floquet model, and a point-gapped tight-binding model. The datasets can be further reduced when certain symmetries exist. A mixed diffusion kernel method is proposed and developed, which could study several topologies at the same time and give hierarchical clustering results. As an application, a novel phase transition process is discovered in a non-Hermitian honeycomb lattice without tedious numerical calculations. This study characterizes band properties without any prior knowledge, which provides a convenient and powerful way to study topology in non-Hermitian systems.