  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. This shows that the diverging
fluctuations of the order parameter near the critical point are driven by a
bifurcation in the underlying drift term, rather than increased stochastic
forcing.
