Enhancing Glassy Dynamics Prediction by Incorporating Displacement from the Initial to Equilibrium State

Understanding the structure-dynamic relationship during the glass transition remains a complex challenge. Recent studies suggest that machine learning (ML) models improve in predicting glassy dynamics when incorporating the distance from the initial to equilibrium states. However, the directional aspect of particle vibrations within the cage has been overlooked. To address this, we propose using vectorial displacement from the initial to equilibrium states as a structural input to ML models. Then, we introduce the Equivariance-Constrained Invariant Graph Neural Network (EIGNN), which uses the displacement parameter to facilitate the structural encoding of the initial configuration and equilibrium configuration. Experimental validation on a three-dimensional (3D) Kob-Andersen system from the GlassBench data set demonstrates that EIGNN significantly enhances the understanding of structure-dynamics correlations and shows robust temperature transferability. Finally, the role of displacement parameters in representing the local bond orientation order is demonstrated through a simplified version of EIGNN, referred to as EIGNN++. These findings underscore the critical role of the orientation of cage dynamics in improving the predictive power of glassy dynamics models.