Rotation-equivariant Graph Neural Networks for Learning Glassy Liquids Representations

Within the glassy liquids community, the use of Machine Learning (ML) to model particles' static structure is currently a hot topic. The state of the art consists in Graph Neural Networks (GNNs), which have a great expressive power but are heavy models with numerous parameters and lack interpretability. Inspired by recent advances in the field of Machine Learning group-equivariant representations, we build a GNN that learns a robust representation of the glass' static structure by constraining it to preserve the roto-translation (SE(3)) equivariance. We show that this constraint not only significantly improves the predictive power but also improves the ability to generalize to unseen temperatures while allowing to reduce the number of parameters. Furthermore, interpretability is improved, as we can relate the action of our basic convolution layer to well-known rotation-invariant expert features. Through transfer-learning experiments we demonstrate that our network learns a robust representation, which allows us to push forward the idea of a learned glass structural order parameter.