Title: Anisotropic Message Passing: Graph Neural Networks with Directional and Long-Range Interactions. Abstract: Graph neural networks have shown great potential for the description of a variety of chemical systems.
However, standard message passing does not explicitly account for long-range and directional interactions, for instance due to electrostatics.
In this work, an anisotropic state based on Cartesian multipoles is proposed as an addition to the existing hidden features.
With the anisotropic state, message passing can be modified to explicitly account for directional interactions.
Compared to existing models, this modification results in relatively little additional computational cost. 
Most importantly, the proposed formalism offers as a distinct advantage the seamless integration of (1) anisotropic long-range interactions, (2) interactions with surrounding fields and particles that are not part of the graph, and (3) the fast multipole method.
As an exemplary use case, the application to quantum mechanics/molecular mechanics (QM/MM) systems is demonstrated.