Equivariant Graph Hierarchy-based Neural Networks

Jiaqi Han, Yu Rong, Tingyang Xu, Wenbing Huang

Keywords: equivariant graph neural network, simulation

TL;DR: We develop a novel hierarchical structure for equivariant graph networks with expressive message passing.

Abstract: 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-UnPool. 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-UnPool leverages the high-level information to update the dynamics of the low-level nodes. As their names imply, both E-Pool and E-UnPool 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.

Community Implementations: [ 3 code implementations](https://www.catalyzex.com/paper/equivariant-graph-hierarchy-based-neural/code)