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.
Bashkova et al. (Fri,) studied this question.