Topological data analysis of large swarming dynamics

Swarms of birds or fishes that use internal chemical energy to form patterns of motion, such as biological swarms and cell groups, have attracted much attention in science and engineering in recent years. This study aims to capture the hierarchical structure formed by such swarms in large-degree-of-freedom systems through topological data analysis (TDA). A large-scale swarm simulation was conducted using the Reynolds' Boids model, which reproduces a swarm of birds by balancing the attraction and repulsion between individuals and the alignment force. As a result, they reported that filament-like, relatively small swarms driven by velocity fluctuations and relatively large swarms driven by density fluctuations occur, even though all particles have the same parameters. On the other hand, these analyses only analyze the internal fluctuation structure of the swarms but do not elucidate the relationships between the swarms. The aim of this study is to reveal the geometrical structure behind swarm pattern series by analyzing them using TDA and Wasserstein distance.