Learning Effective SDEs from Brownian Dynamics Simulations of Colloidal Particles

TL;DR

This paper develops a data-driven reduced stochastic model for colloidal crystallization using manifold learning and deep learning, accurately capturing both simulation and experimental dynamics.

Contribution

It introduces a novel combination of Diffusion Maps and deep learning to identify effective SDEs from simulation data, applicable to various particle systems.

Findings

The learned eSDE accurately encodes Brownian dynamics.

The reduced model captures experimental colloidal crystallization dynamics.

The approach is broadly applicable to particle system experiments.

Abstract

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.