Unsupervised Manifold Clustering of Topological Phononics

Classification of topological phononics is challenging due to the lack of universal topological invariants and the randomness of structure patterns. Here, we show the unsupervised manifold learning for clustering topological phononics without any a priori knowledge, neither topological invariants nor supervised trainings, even when systems are imperfect or disordered. This is achieved by exploiting the real-space projection operator about finite phononic lattices to describe the correlation between oscillators. We exemplify the efficient unsupervised manifold clustering in typical phononic systems, including a one-dimensional Su-Schrieffer-Heeger-type phononic chain with random couplings, amorphous phononic topological insulators, higher-order phononic topological states, and a non-Hermitian phononic chain with random dissipations. The results would inspire more efforts on applications of unsupervised machine learning for topological phononic devices and beyond.