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Understanding the dynamic processes of the glassy system continues to bechallenging. Recent advances have shown the power of graph neural networks(GNNs) for determining the correlation between structure and dynamics in theglassy system. These methods treat the glassy system as a topological graph.However, the inherent "smoothness" property of the dynamics on the graph(variation of dynamics over the graph) is ignored, resulting in a deterioratedperformance of GNN for dynamic predictions over various time scales. In thispaper, we first present an experimental investigation assessing the smoothnesspatterns of particle dynamics from the graph perspective. The results indicatethat the long-time dynamics exhibit a smoother property on the graph, while theshort-time dynamics reveal a distinctly non-smooth pattern. To establish therelationship between the static structure and dynamics with differentsmoothness patterns, we propose a novel geometry-enhanced graph neural network(Geo-GNN) model. The Geo-GNN architecture consists of a geometry featureencoder that incorporates rotation-invariant distances and angles to enhancegeometric feature learning and a geometry-enhanced aggregation block that canadaptively learn the underlying smoothness patterns during message passing.Experimental results demonstrate that our method is able to capture theinherent smoothness pattern of particles and outperforms state-of-the-artbaselines in predicting the dynamics across all time scales. A subsequent studyhas revealed that geometric features are critical for the model to accuratelycapture smoothness patterns in dynamics. Our research not only refines themethod for predicting glassy dynamics but also provides a new lens throughwhich to investigate the issue of causality regarding dynamical heterogeneityin glasses.

Geometry-enhanced graph neural network for learning the smoothness of glassy dynamics from static structure