  Equivariant Graph neural Networks (EGNs) are powerful in characterizing the
dynamics of multi-body physical systems. Existing EGNs conduct flat message
passing, which, yet, is unable to capture the spatial/dynamical hierarchy for
complex systems particularly, limiting substructure discovery and global
information fusion. In this paper, we propose Equivariant Hierarchy-based Graph
Networks (EGHNs) which consist of the three key components: generalized
Equivariant Matrix Message Passing (EMMP) , E-Pool and E-UpPool. In particular,
EMMP is able to improve the expressivity of conventional equivariant message
passing, E-Pool assigns the quantities of the low-level nodes into high-level
clusters, while E-UpPool leverages the high-level information to update the
dynamics of the low-level nodes. As their names imply, both E-Pool and E-UpPool
are guaranteed to be equivariant to meet physic symmetry. Considerable
experimental evaluations verify the effectiveness of our EGHN on several
applications including multi-object dynamics simulation, motion capture, and
protein dynamics modeling.
