Differential Equation Discovery of Robotic Swarm as Active Matter

This chapter delves into the application of differential equation discovery to model robotic swarms as active matter, a class of systems characterized by collective behavior driven by self-assembly. By leveraging machine learning methods, particularly physics-informed neural networks and equation discovery techniques, the authors propose a universal data-driven approach to derive models that reflect the behavioral characteristics of these systems. The chapter investigates several problems, including the motion of a single particle in 2D without external forcing and the extraction of displacement fields from experimental data using computer vision methods to derive partial differential equations (PDEs). The EPDE framework, specifically designed for this purpose, integrates seamlessly with the TEDEouS solver to compare the solutions of discovered equations with experimental data. The chapter also discusses the challenges and uncertainties in modeling active matter systems, highlighting the need for expert consultation and data quality improvement. The findings underscore the potential of contemporary equation discovery techniques to enhance our understanding of active matter systems and highlight areas for future improvement.