Learning Physical Dynamics with Subequivariant Graph Neural Networks
This work improves physical simulation accuracy for applications like robotics and computer graphics, though it is incremental as it builds on existing GNN methods.
The paper tackled the challenge of learning physical dynamics by addressing insufficient or excessive symmetry in existing models and handling diverse object properties, proposing a Subequivariant Graph Neural Network that achieved over 3% improvement in contact prediction accuracy on Physion and 2X lower rollout MSE on RigidFall compared to state-of-the-art GNN simulators.
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.