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

TL;DR

This paper introduces hierarchical, equivariant graph neural networks that effectively model and predict complex collective behaviors in vortex clusters and microswimmers by capturing long-range interactions and preserving physical invariances.

Contribution

The authors develop a novel hierarchical and equivariant GNN framework that improves long-range interaction modeling in collective motion systems, outperforming traditional GNNs.

Findings

Accurately predicts local and global behaviors in vortex and microswimmer systems.

Conserves Hamiltonian in vortex simulations over long times.

Predicts transition from aggregation to swirling in microswimmer populations.

Abstract

Data-driven modeling of collective dynamics is a challenging problem because emergent phenomena in multi-agent systems are often shaped by long-range interactions among individuals. For example, in bird flocks and fish schools, long-range vision and flow coupling drive individual behaviors across the collective. 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. For the point vortices, we define a local graph of vortices within a cluster and a global graph of interactions between clusters. For the microswimmers, we define a local graph around each microswimmer and a global graph that groups long-range interactions. We then combine this hierarchy of graphs with an approach that enforces equivariance to rotations and translations. This combination results in a significant improvement over a fully-connected GNN. For point vortices, our method conserves the Hamiltonian over long times, and, for microswimmers, our method predicts the transition from aggregation to swirling.