Relaxing Continuous Constraints of Equivariant Graph Neural Networks for Physical Dynamics Learning

Understand

Incorporating Euclidean symmetries (e.g.

• rotation equivariance) as inductive biases into graph neural networks has improved their generalization ability and data efficiency in unbounded physical dynamics modeling.
• However, in various scientific and engineering applications, the symmetries of dynamics are frequently discrete due to the boundary conditions.
• Thus, existing GNNs either overlook necessary symmetry, resulting in suboptimal representation ability, or impose excessive equivariance, which fails to generalize to unobserved symmetric dynamics.