  Effectively predicting molecular interactions has the potential to accelerate
molecular dynamics by multiple orders of magnitude and thus revolutionize
chemical simulations. Graph neural networks (GNNs) have recently shown great
successes for this task, overtaking classical methods based on fixed molecular
kernels. However, they still appear very limited from a theoretical
perspective, since regular GNNs cannot distinguish certain types of graphs. In
this work we close this gap between theory and practice. We show that GNNs with
spherical representations are indeed universal approximators for predictions
that are invariant to translation, and equivariant to permutation and rotation.
We then discretize such GNNs via directed edge embeddings and two-hop message
passing, and incorporate multiple structural improvements to arrive at the
geometric message passing neural network (GemNet). We demonstrate the benefits
of the proposed changes in multiple ablation studies. GemNet outperforms
previous models on the COLL, MD17, and OC20 datasets by 34%, 41%, and 20%,
respectively, and performs especially well on the most challenging molecules.
Our implementation is available online.
