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Effectively predicting molecular interactions has the potential to acceleratemolecular dynamics by multiple orders of magnitude and thus revolutionizechemical simulations. Graph neural networks (GNNs) have recently shown greatsuccesses for this task, overtaking classical methods based on fixed molecularkernels. However, they still appear very limited from a theoreticalperspective, since regular GNNs cannot distinguish certain types of graphs. Inthis work we close this gap between theory and practice. We show that GNNs withdirected edge embeddings and two-hop message passing are indeed universalapproximators for predictions that are invariant to translation, andequivariant to permutation and rotation. We then leverage these insights andmultiple structural improvements to propose the geometric message passingneural network (GemNet). We demonstrate the benefits of the proposed changes inmultiple ablation studies. GemNet outperforms previous models on the COLL,MD17, and OC20 datasets by 34%, 41%, and 20%, respectively, and performsespecially well on the most challenging molecules. Our implementation isavailable online.

GemNet: Universal Directional Graph Neural Networks for Molecules