Unsupervised Learning of non‐Hermitian Photonic Bulk Topology

Abstract 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.