Unsupervised machine learning for supercooled liquids

Unraveling dynamic heterogeneity in supercooled liquids from structural information is one of the grand challenges of physics. In this work, we introduce an unsupervised machine learning approach based on a time-lagged autoencoder (TAE) to elucidate the effect of structural features on the long-term dynamics of supercooled liquids. The TAE uses an autoencoder to reconstruct features at time $t + \Delta t$ from input features at time $t$ for individual particles, and the resulting latent space variables are considered as order parameters. In the Kob-Andersen system, with a $\Delta t$ about a thousand times smaller than the relaxation time, the TAE order parameter exhibits a remarkable correlation with the long-time propensity. We find that short-range radial features correlate with the short-time dynamics, and medium-range radial features correlate with the long-time dynamics. This shows that fluctuations of medium-range structural features contain sufficient information about the long-time dynamic heterogeneity, consistent with some theoretical predictions.