Repo for Differential Equation Ensembles Discovery for Modeling Active Matter Based on Robotic Swarm Data submitted to MAKE journal This work implements the EPDE+SAGE methodology for discovering interpretable stochastic differential equations from experimental or simulated active matter data. The approach bridges discrete agent-based descriptions to continuum field theories through three hierarchical modeling levels:
- Microscopic — Individual agent dynamics via ODEs with interaction forces
d²rₖ/dt² = Fᵢₙₜ + Σ Fₑₓₜ - Mesoscopic — Collective order parameters via coupled SDEs
dΦ = A(Φ)dt + B(Φ)∘dWₜ - Macroscopic — Continuum field evolution via SPDEs
∂u/∂t = ℒ_μ[u] + ℒ_σ[u]