The relationship between structure and dynamics in glassy fluids remains an intriguing open question. Recent work has shown impressive advances in our ability to predict local dynamics using structural features, most notably due to the use of advanced machine learning techniques. Here, we explore whether a simple linear regression algorithm combined with intelligently chosen structural order parameters can reach the accuracy of the current, most advanced machine learning approaches for predicting dynamic propensity. To achieve this, we introduce a method to pinpoint the cage state of the initial configuration-i.e., the configuration consisting of the average particle positions when particle rearrangement is forbidden. We find that, in comparison to both the initial state and the inherent state, the structure of the cage state is highly predictive of the long-time dynamics of the system. Moreover, by combining the cage state information with the initial state, we are able to predict dynamic propensities with unprecedentedly high accuracy over a broad regime of time scales, including the caging regime.
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