A graph-neural-network framework for forecasting collective dynamics in multi-agent systems that combines a two-scale hierarchy of local and global graphs with a mapping into a rotation- and translation-invariant subspace, letting any GNN backbone respect Euclidean symmetry while capturing both short- and long-range interactions. Learners study how enforcing hierarchy and equivariance by construction (rather than learning them from data) improves long-horizon accuracy, conserves physical invariants such as the point-vortex Hamiltonian, and predicts emergent transitions like microswimmer aggregation-to-swirling.
Introduces hierarchical equivariant graph neural networks (HE-GNN) for data-driven forecasting of collective motion in multi-agent systems whose interaction laws are unknown. The method builds a two-…