标题： 分层等变图神经网络用于预测涡旋团簇和微游泳者的集体运动 显示英文标题

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

摘要： 基于数据的集体动力学建模是一个具有挑战性的问题，因为多智能体系统中的涌现现象通常由个体之间的长程相互作用塑造。 例如，在鸟群和鱼群中，长程视觉和流体耦合驱动了个体行为在整个群体中的传播。 这种集体运动可以通过图神经网络（GNNs）来建模，但当图变得很大时，GNNs往往难以捕捉长程相互作用并且经常失败。 在这里，我们构建了分层且等变的图神经网络，并展示了这些GNNs能够准确预测具有集体运动系统的局部和全局行为。 作为代表性例子，我们将这种方法应用于点涡旋集群和微游动群体的模拟。 对于点涡旋，我们定义了集群内涡旋的局部图以及集群间相互作用的全局图。 对于微游动生物，我们定义了每个微游动生物周围的局部图和一个将长程相互作用分组的全局图。 然后，我们将这一层次结构的图与一种强制旋转和平移等变性的方法相结合。 这种组合相较于全连接的GNN有了显著改进。 对于点涡旋，我们的方法能够在长时间内保持哈密顿量守恒；对于微游动生物，我们的方法能够预测从聚集到旋转的转变。 显示英文摘要

摘要： 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.