Beyond GNNs: Enhanced Topological Classification, Discovery, and Prediction*

Topological materials have transformative potential across various technological areas, and there has been significant interest in accurately predicting these properties through machine learning, especially using Graph Neural Networks (GNNs). These graph models, and to a larger extent the Message Passing Neural Network variants, have been shown to work well for many applications. However, they face critical limitations in simultaneously modeling local and global atomic interactions, capturing mid-sized structural motifs, and approximating relevant classes of functions due to their bounded expressive power.

To address these challenges, we designed new representations based on isometry invariants of periodic point sets, and improved model architectures inspired by folklore variants of the Weisfeiler-Lehman graph isomorphism tests. These modifications have demonstrated substantial enhancements on benchmark materials datasets. In this talk, we report on the state-of-the-art models we trained for predicting topological classifications and highlight the practical insights and applications gained from our models.