Prediction and classification in equation-free collective motion dynamics

Modeling the complex collective behavior is a challenging issue in several material and life sciences. The collective motion has been usually modeled by simple interaction rules and explained by global statistics. However, it remains difficult to bridge the gap between the dynamic properties of the complex interaction and the emerging group-level functions. Here we introduce decomposition methods to directly extract and classify the latent global dynamics of nonlinear dynamical systems in an equation-free manner, even including complex interaction in few data dimensions. We first verified that the basic decomposition method can extract and discriminate the dynamics of a well-known rule-based fish-schooling (or bird-flocking) model. The method extracted different temporal frequency modes with spatial interaction coherence among three distinct emergent motions, whereas these wave properties in multiple spatiotemporal scales showed similar dispersion relations. Second, we extended the basic method to map high-dimensional feature space for application to actual small-dimensional systems complexly changing the interaction rules. Using group sports human data, we classified the dynamics and predicted the group objective achievement. Our methods have a potential for classifying collective motions in various domains which obey in non-trivial dominance law known as active matters.Author summary: Modeling complex collective motions is a challenging problem such as in biology, physics, and human behavior because the rules governing the motion are sometimes unclear. Then, researchers have usually used simple interaction model and explain global statistics. However, it remains difficult to bridge the gap between the dynamic properties of the complex interaction and the group-level functions. This study develops an effective framework to extract the dynamics of collective motion from data by data-driven modeling. Compared with conventional methods, our method can be applied to cases with the small numbers of group members or transient and complex changes of the behavioral rules. Our methods successfully discriminated group movements of well-known fish-schooling models and predicted the achievement of a group objective from actual basketball players’ position data. Our methods have a potential for outcome prediction and classification for various unsolved and complex collective motions such as in biology and physics.