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Understanding the physics of supercooled liquids near glassy transitionremains one of the major challenges in condensed matter science. There has beenlong recognized that supercooled liquids have spatially dynamical heterogeneitywhose dynamics in some regions of the sample could potentially be orders ofmagnitude faster than the dynamics in other regions only a few nanometers away.However, to identify such domain structures both structurally andconfigurationally in a consistent fashion and the connection between structuresand dynamics remains elusive. A new approach to classify these spatialheterogeneities of supercooled liquids is developed. Using average weightedcoordination numbers (WCNs) of particles as features for the PrincipleComponent Analysis (PCA) and Gaussian Mixture (GM) clustering, a representationof the feature space to perform GM clustering is constructed after applying PCAto WCNs. Nano-domains or aggregated clusters are found in configurational(real) space by direct mapping the identities of clusters in the feature(structural) space with some classification uncertainties. These uncertaintiescan be improved by a co-learning strategy to transmit information between thestructural space and configurational space iteratively until convergence. Thedomains are indeed found to be remarkably consistent in both spaces over longtimes as well as measured to have heterogeneous dynamics. Using such aclassification scheme the order parameter time correlation function follows thenon-conserved order parameter scaling law, which indicates that such domainsare the result of liquid-liquid phase separation after quenching.

A dual-space classification scheme of spatial heterogeneities in 2D monatomic supercooled liquids