Trainable control of active nematic defect dynamics using imperfect feedback and artificial intelligence

Learning how to control active matter systems is a key step to understanding how living systems regulate their own active components and how we might engineer new functional materials. Top-down approaches to this task which require full knowledge of the system’s physics, such as optimal control, cannot plausibly be implemented by biological feedback loops.  This motivates searching for new training protocols that do not require perfect system specification.  Inspired by advances in training neural networks using imperfect error signal propagation, we introduce an imperfect, thermodynamically-motivated learning algorithm for controlling non-equilibrium systems. In a supervised learning setup, our algorithm uses only local comparisons between the system’s free energy and that of a target trajectory to provide increments in a control parameter guiding the system. Surprisingly for these driven systems, these equilibrium free energy comparisons can provide sufficient information for convergence.  We characterize the conditions under which convergence happens, and we demonstrate this learning rule on the non-trivial control task of pulling defects in active nematic systems along desired trajectories.  This illustrates how a coarse projection of the full system state can allow iterative improvement of a non-equilibrium control process, which can guide future investigations into biologically plausible learning routines.  In addition to imperfect feedback, we also explore controlling active nematic defects using reinforcement learning – a “trial and error”-based machine learning technique that eschews any knowledge of the system’s physics.  This practical method can be useful for developing refined experimental control over living and engineered active matter systems.