Abstract
The control of far-from-equilibrium physical systems, including active materials, requires advanced control strategies due to the non-linear dynamics and long-range interactions between particles, preventing explicit solutions to optimal control problems. In such situations, Reinforcement Learning (RL) has emerged as an approach to derive suitable control strategies. However, for active matter systems, it is an important open question how the mathematical structure and the physical properties determine the tractability of RL. In this paper, we demonstrate that RL can only find good mixing strategies for active matter systems that combine attractive and repulsive interactions. Using analytic results from dynamical systems theory, we show that combining both interaction types is indeed necessary for the existence of mixing-inducing hyperbolic dynamics and therefore the ability of RL to find homogeneous mixing strategies. In particular, we show that for drag-dominated translational-invariant particle systems, mixing relies on combined attractive and repulsive interactions. Therefore, our work demonstrates which experimental developments need to be made to make protein-based active matter applicable, and it provides some classification of microscopic interactions based on macroscopic behavior.
Highlights
The control of far-from-equilibrium physical systems, including active materials, requires advanced control strategies due to the non-linear dynamics and long-range interactions between particles, preventing explicit solutions to optimal control problems
We can observe that agents failing due to some instabilities, as seen by a sharp drop in the reward, can recover due to using Population Based Training (PBT)
This paper analyzed a challenging control problem arising for active matter components, where control cannot be exerted over individual agents or particles but merely over their pairwise interaction
Summary
The control of far-from-equilibrium physical systems, including active materials, requires advanced control strategies due to the non-linear dynamics and long-range interactions between particles, preventing explicit solutions to optimal control problems. While some limited control was achieved, such as the ability to generate simple fluid flows,[13,14,15,16,32] achieve global particle momentum,[33] and accelerated equilibration of otherwise glassy systems,[17] control strategies for more complex scenarios are absent The reason for this challenging behavior is that active matter systems are interaction-dominated, so strategies have to exert indirect control via agent–agent interactions rather than. For our model of active particles, we observe that while RL fails to learn good strategies if only attractive or repulsive interactions are available, RL finds good strategies if attractive and repulsive interactions can be combined We analyze this puzzling behavior using dynamical systems theory, theory to hyperbolic dynamics and Anosov diffeomorphisms,[34] to prove that mixed interactions are necessary to render the problem solvable. Provide a guideline to make protein-based active matter applicable and answer the question of how different interactions can lead to macroscopic behavior asked in a recent review.[18]
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