  Unraveling the relation between structural information and the dynamic
properties of supercooled liquids is one of the grand challenges of physics.
Dynamic heterogeneity, characterized by the propensity of particles, is often
used as a proxy for the dynamic slowing down. 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-time dynamic
heterogeneity 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
radial features on all length-scales are required to capture the long-time
dynamics, consistent with recent simulations. This shows that fluctuations of
structural features contain sufficient information about the long-time dynamic
heterogeneity.
