Data-driven stochastic modeling of coarse-grained dynamics with finite-size effects using Langevin regression

Understand

Obtaining coarse-grained models that accurately incorporate finite-size effects is an important open challenge in the study of complex, multi-scale systems.

• We apply Langevin regression, a recently developed method for finding stochastic differential equation (SDE) descriptions of realistically-sampled time series data, to understand finite-size effects in the Kuramoto model of coupled oscillators.
• We find that across the entire bifurcation diagram, the dynamics of the Kuramoto order parameter are statistically consistent with an SDE whose drift term has the form predicted by the Ott-Antonsen ansatz in the $N\to \infty$ limit.
• We find that the diffusion term is nearly independent of the bifurcation parameter, and has a magnitude decaying as $N^{-1/2}$, consistent with the central limit theorem.