Multi-Scale Modeling and Predictive Control of Active Brownian Particles

Abstract: Active Brownian particles (ABPs) function as self-driving agents that display non-equilibrium behavior through their pairwise interactions which lead to phase separation and vortex patterns in both soft matter and living systems. A multiscale approach needs to link particle-level random motion to collective density evolution for proper management of these dynamic systems. Our research delivers a unified control system for ABP groups through particle-based simulation and spectral continuum modeling alongside model predictive control and deep learning forecasting. The N-particle Brownian dynamics simulations implement Weeks-Chandler-Andersen potential to model excluded-volume interactions while incorporating thermal noise and angular velocity modulation with wavelength $\lambda$. The forced advection-diffusion equation describes the coarse-grained density evolution which the FTCS spectral space solver solves. A new MPC approach uses complex-valued density states to minimize immediate tracking errors against sinusoidal spatial setpoints with actuator limits and control penalties. The hybrid deep neural network combines Conv1D and LSTM and multi-head attention to learn future density profiles from simulated snapshot sequences.