Learning continuum-level closures for control of interacting active particles.

Area of Science:

• Physics
• Materials Science
• Control Theory

Background:

• Active matter swarms are difficult to steer, especially in crowded systems where individual agent control is impractical.
• Existing control methods require fast, accurate, and differentiable models, which are challenging to develop for complex active matter dynamics.

Purpose of the Study:

• To develop a learning-for-control framework for steering active matter swarms using macroscopic fields.
• To address the challenge of constructing accurate continuum closures for active matter dynamics.

Main Methods:

• A Universal Differential Equation (UDE) framework was employed, representing the continuum as an advection-diffusion equation.
• A neural operator was used to learn the advection term, providing closure relations for microscopic effects.
• The learned continuum model was integrated into Model Predictive Control (MPC) for agent-simulation control.

Main Results:

• The framework successfully learned continuum closures from agent simulations for active Brownian particles.
• Demonstrated precise control by dynamically exchanging particle densities between groups.
• Achieved simultaneous control of particle density and mean flux to follow a sinusoidal profile.

Conclusions:

• The UDE-based learning-for-control framework offers a powerful method for steering active matter swarms.
• This approach facilitates the development of programmable materials with controllable dynamic properties.
• The framework ensures adherence to physical laws while learning complex dynamics from data.