Hierarchical equivariant graph neural networks for forecasting collective motion in vortex clusters and microswimmers

Data-driven modeling of collective dynamics is a challenging problem because emergent phenomena in multi-agent systems are often shaped by short- and long-range interactions among individuals. For example, in bird flocks and fish schools, flow coupling plays a crucial role in emergent collective behavior. Such collective motion can be modeled using graph neural networks (GNNs), but GNNs struggle when graphs become large and often fail to capture long-range interactions. Here, we construct hierarchical and equivariant GNNs, and show that these GNNs accurately predict local and global behavior in systems with collective motion. As representative examples, we apply this approach to simulations of clusters of point vortices and populations of microswimmers. In these systems, our approach is more accurate and faster than a fully-connected GNN. Specifically, only our approach conserves the Hamiltonian for the point vortices and only our approach predicts the transition from aggregation to swirling for the microswimmers.