Graph Neural Networks that incorporate Physical Structure

There has been considerable interest in applying neural networks to physical systems that can be represented by graphs. While this is typically done using message-passing neural networks, these networks are strictly limited in their expressivity and there is no obvious way to include our knowledge of physical structure into the network. To address this need, we introduce automorphism-based graph neural networks (Autobahn), a new family of graph neural networks. Whereas in most graph neural networks neurons correspond to individual bonds or edges, in Autobahn neurons correspond to graph substructures. This allows us to incorporate domain knowledge into the design of the network. Moreover, by applying local convolutions that are equivariant to each subgraph's automorphism group, we construct neurons whose action reflects the natural way that a physical substructure transforms. Specific choices of local neighborhoods and subgraphs recover existing graph neural network architectures such as message passing neural networks, but our formalism also encompasses novel architectures: as an example, we introduce a graph neural network that decomposes the graph into paths and cycles. We validate our approach by applying Autobahn to molecular graphs, where we achieve competitive results.