拓扑音位学的无监督流形聚类
Unsupervised Manifold Clustering of Topological Phononics
摘要：
拓扑声子的分类由于缺乏普适的拓扑不变量和结构模式的随机性而具有挑战性。在这里，我们展示了用于聚类拓扑声子的无监督流形学习，没有任何先验知识，既没有拓扑不变量，也没有监督训练，即使系统是不完美或无序的。这是通过利用有限声子晶格的实空间投影算子来描述振子之间的相关性。我们在典型的声子系统中，包括一维随机耦合的Su-Schrieffer-Heeger型声子链、非晶声子拓扑绝缘体、高阶声子拓扑态和随机耗散的非Hermitian声子链，研究了有效的无监督流形聚类.这些结果将激励人们在拓扑声子设备及其他领域的无监督机器学习应用方面做出更多努力。
英文摘要：
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 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 one-dimensional Su-Schrieffer-Heeger-type phononic chain with random couplings, amorphous phononic topological insulators, higher-order phononic topological states and 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.
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