Differential Equation Ensemble Discovery for Modeling Active Matter Based on Robotic Swarm Data

Active matter actively searches for models that allow them to connect the behavior of multiple agents to particle system with a physical law. However, the arsenal of models used to model active matter systems is very restricted. Modern differential equation discovery approaches allow one to extract governing equations from data for a single particle in the form of the ODE. However, there is still the question of how to model at the meso- and macroscales. This paper presents a data-driven framework for extracting the governing physical laws of a hardware-made swarm across multiple scales of organization. Using the EPDE framework, we transition from a discrete, chaotic trajectory of individual agents to a continuous, effective field theory of the collective. We show that augmenting the symbolic search space with interaction-aware tokens allowed for the derivation of stochastic partial differential equations (SDEs) that significantly outperformed baseline deterministic models (reducing CRPS by up to 10%). Additionally, we derive a system of SPDEs that governs the macroscale displacement field.