Learning Effective SDEs from Brownian Dynamics Simulations of Colloidal Particles

The identification of nonlinear dynamical systems from experimental time series and image series data became an important research theme in the early 1990s [25, 37, 36]. After lapsing for almost two decades, it is now experiencing a spectacular rebirth. A key element of the older work was the use of neural architectures [14, 37] (recurrent, convolutional, ResNet) motivated by traditional numerical analysis algorithms. Importantly, such architectures allow researchers to identify effective, coarse-grained, mean-field type evolution models from fine-scale (atomistic, molecular, agent-based) data [29, 5]. In this paper, we identify coarse-grained, effective stochastic differential equations (eSDE) for colloidal particle selfassembly based onfine-grained, Brownian dynamics simulations under the influence of electric fields [51, 11]. We demonstrate that the identified eSDE encodes accurately the physics of the Brownian Dynamic simulations and captures the dynamics of corresponding experimental data. Those experiments have previously been shown to quantitatively match to BD simulations at equilibrium in terms of time-averaged distribution functions [11, 18, 20]. Figure 1 shows a sample path of a latent space trajectory {t, φ(t)}