Macroscopic modelling and analysis based on microscopic models for swarm systems

Swarm systems, whether biological or artificial, often exhibit higher efficiency, robustness, and flexibility than individual entities, enabling them to accomplish tasks that individuals cannot achieve. However, there is still no comprehensive and universal modelling and analysis methodology for swarm systems. This paper presents a bidirectional closed-loop modelling framework that combines microscopic models with macroscopic modelling. In this approach, a probabilistic finite state machine is first used to establish the microscopic model, and a macroscopic model is then constructed based on rate equations. Finally, the evolution of the macroscopic model provides feedback to refine the configuration of the microscopic model. Through a simulation case study of infectious disease transmission in a closed environment, the effectiveness of the macroscopic model is validated. Simulation results indicate that our method emphasizes the derivation process from microscopic to macroscopic modelling, overcoming the limitations of studies that focus solely on either the micro or macro level. The macroscopic model not only provides predictions of the long-term behavior of swarm systems but also facilitates optimization. Furthermore, optimization methods based on the macroscopic model can enhance system performance and decision-making efficiency without increasing system complexity. Our research offers a novel perspective on swarm system modelling and analysis, providing important theoretical support for the analysis and optimization of swarm behaviors in practical applications.