Equivariant Graph Hierarchy-Based Neural Networks
This work addresses the limitation of existing EGNs in capturing spatial/dynamical hierarchies for complex physical systems, which is incremental as it builds on prior EGN methods.
The paper tackled the problem of flat message passing in Equivariant Graph Neural Networks (EGNs) limiting hierarchy capture in complex systems, and proposed Equivariant Hierarchy-based Graph Networks (EGHNs) with components like EMMP, E-Pool, and E-UpPool, showing effectiveness in applications such as multi-object dynamics simulation, motion capture, and protein dynamics modeling.
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.