Graph Neural Networks (GNNs) have become a prevailing tool for learning
physical dynamics. However, they still encounter several challenges: 1)
Physical laws abide by symmetry, which is a vital inductive bias accounting for
model generalization and should be incorporated into the model design. Existing
simulators either consider insufficient symmetry, or enforce excessive
equivariance in practice when symmetry is partially broken by gravity. 2)
Objects in the physical world possess diverse shapes, sizes, and properties,
which should be appropriately processed by the model. To tackle these
difficulties, we propose a novel backbone, Subequivariant Graph Neural Network,
which 1) relaxes equivariance to subequivariance by considering external fields
like gravity, where the universal approximation ability holds theoretically; 2)
introduces a new subequivariant object-aware message passing for learning
physical interactions between multiple objects of various shapes in the
particle-based representation; 3) operates in a hierarchical fashion, allowing
for modeling long-range and complex interactions. Our model achieves on average
over 3% enhancement in contact prediction accuracy across 8 scenarios on
Physion and 2X lower rollout MSE on RigidFall compared with state-of-the-art
GNN simulators, while exhibiting strong generalization and data efficiency.

本文提出了一种新颖的基础方法，称为 Subequivariant Graph Neural Network，并解决了在物理动力学中如何将物理定律所包含的对称性协同模型设计以及模型如何处理物理世界中不同形状、尺寸和属性的物体等问题。该模型在 8 个场景的 Physion 数据集中，平均接触预测准确率有超过 3％的提高，在 RigidFall 数据集中有 2 倍的低回滚均方误差，并展现出强大的泛化能力和数据效率。