Modelling multiscale collective behavior with Gaussian processes

Collective behavior is characterized by the emergence of large-scale phenomena from local interactions. It is found in many contexts, including political movements, fads and fashions, and animal grouping. In this paper, we aim to elucidate the mechanisms that underlie observed collective behavior by developing a novel mathematical framework based on equation-free modelling procedures and Gaussian process regression. This allows us to circumvent the possible lack of formal mathematical links between scales and instead use statistical emulation to learn an empirical Fokker-Planck equation. Our approach advances our ability to understand how complex systems function at both the individual and collective level when a formal mathematical description of macroscale dynamics is unavailable.