  We construct a reduced, data-driven, parameter dependent effective Stochastic
Differential Equation (eSDE) for electric-field mediated colloidal
crystallization using data obtained from Brownian Dynamics Simulations. We use
Diffusion Maps (a manifold learning algorithm) to identify a set of useful
latent observables. In this latent space we identify an eSDE using a deep
learning architecture inspired by numerical stochastic integrators and compare
it with the traditional Kramers-Moyal expansion estimation. We show that the
obtained variables and the learned dynamics accurately encode the physics of
the Brownian Dynamic Simulations. We further illustrate that our reduced model
captures the dynamics of corresponding experimental data. Our dimension
reduction/reduced model identification approach can be easily ported to a broad
class of particle systems dynamics experiments/models.
