Equivariant Graph Hierarchy-Based Neural Networks

2022/02/22 by Jiaqi Han, Han, Jiaqi, Wenbing Huang +5 · 4 citations
Computer Science · #FOS: Computer and information sciences #Machine Learning (cs.LG) #cs.LG

paper · pdf · doi:10.48550/arxiv.2202.10643

20 pages

arxiv created 2022/10/15 · arxiv updated 2022/10/18

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-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.

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• Learning Equivariant Functions via Quadratic Forms
• Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learning
• Geometric Hyena Networks for Large-scale Equivariant Learning
• Equi-Euler GraphNet: An Equivariant, Temporal-Dynamics Informed Graph Neural Network for Dual Force and Trajectory Prediction in Multi-Body Systems

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