Learning Effective SDEs from Brownian Dynamics Simulations of Colloidal Particles. (arXiv:2205.00286v2 [math.DS] UPDATED)

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 …

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