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.

翻译：我们利用布朗动力学模拟数据，构建了一个数据驱动、参数依赖的约化有效随机微分方程（eSDE），用于描述电场介导的胶体结晶过程。采用扩散映射（一种流形学习算法）识别一组有效的潜在可观测变量。在潜在空间中，我们利用受数值随机积分器启发的深度学习架构来识别eSDE，并将其与传统的Kramers-Moyal展开估计进行对比。结果表明，所获得的变量及学习到的动力学过程能够准确编码布朗动力学模拟的物理特性。我们进一步说明，该约化模型能够捕捉相应实验数据的动力学行为。我们的降维/约化模型识别方法可便捷地推广至广泛的粒子系统动力学实验/模型中。