  We consider representation learning of 3D molecular graphs in which each atom
is associated with a spatial position in 3D. This is an under-explored area of
research, and a principled message passing framework is currently lacking. In
this work, we conduct analyses in the spherical coordinate system (SCS) for the
complete identification of 3D graph structures. Based on such observations, we
propose the spherical message passing (SMP) as a novel and powerful scheme for
3D molecular learning. SMP dramatically reduces training complexity, enabling
it to perform efficiently on large-scale molecules. In addition, SMP is capable
of distinguishing almost all molecular structures, and the uncovered cases may
not exist in practice. Based on meaningful physically-based representations of
3D information, we further propose the SphereNet for 3D molecular learning.
Experimental results demonstrate that the use of meaningful 3D information in
SphereNet leads to significant performance improvements in prediction tasks.
Our results also demonstrate the advantages of SphereNet in terms of
capability, efficiency, and scalability. Our code is publicly available as part
of the DIG library (https://github.com/divelab/DIG).
