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.
翻译:神经网络(GNNs)已成为学习物理动态的常用工具。然而,它们仍面临若干挑战:(1) 物理法符合对称,这是模型一般化的重要导导偏向性,对于模型一般化而言,应将其纳入模型设计。现有的模拟器或者考虑对称不充分,或者当对称部分因重力而部分断裂时在实际中强制执行过分的等同性。(2) 物理世界中的物体具有不同的形状、大小和特性,应当由模型加以适当处理。为了解决这些困难,我们提议了一个新的主干线,即次等等异图形神经网络。这个主干线通过考虑外部领域(例如重力,即通用近似能力保持理论上的外部领域),可以放松对次等异性对等性以至次异性。(2) 引入一种新的次等异性物体感信息,传递给学习粒子代表面不同形状多个物体之间的物理互动;(3) 以等级方式运行,允许模型进行远程和复杂互动的模型。为了应对这些困难,我们的模式可以实现平均超过3%的联度预测精确度,在Phyalsion-Faxxxxxxxx ValalalalxxGnalxxxxxxxxxxxxxxxxxxxxxxGyalpalpalpalpalpalpalpalpalxxxxxxxxxx。