标题： 微尺度最优控制的普遍对称性 显示英文标题

标题： Universal symmetry of optimal control at the microscale

摘要： 优化驱动过程的能量效率为理解基本物理提供了有价值的见解，并在从生物过程到机器和机器人设计的众多应用中具有关键重要性。在微尺度上，了解最优驱动协议尤其有价值，因为在该尺度上能量供应通常有限。在这里，我们实验和理论上研究了在有限时间和给定距离内移动承载负载的势能的典型优化问题，以使所需功最小。考虑周围流体中的记忆效应是向更现实系统迈进的重要一步，这在现实应用中是普遍存在的。因此，我们的实验是在粘性和粘弹性介质中进行的，这些是微尺度上合成和生物过程的典型环境。尽管两种流体中的协议存在显著差异，但我们发现最优控制协议和相应的平均粒子轨迹始终遵循时间反演对称性。我们表明，这种对称性出人意料地适用于远离热平衡的一类过程，在各种系统中都普遍成立，包括活性、颗粒和长程关联介质在其线性区域。揭示的对称性为最优控制提供了一个严格且通用的标准，大大促进了在广泛系统中寻找节能传输策略的搜索。使用机器学习算法，我们证明了对时间反演对称性的算法利用可以显著提高数值优化算法的性能。 显示英文摘要

摘要： Optimizing the energy efficiency of driving processes provides valuable insights into the underlying physics and is of crucial importance for numerous applications, from biological processes to the design of machines and robots. Knowledge of optimal driving protocols is particularly valuable at the microscale, where energy supply is often limited. Here we investigate experimentally and theoretically the paradigmatic optimization problem of moving a potential carrying a load through a fluid, in a finite time and over a given distance, in such a way that the required work is minimal. An important step towards more realistic systems is the consideration of memory effects in the surrounding fluid, which are ubiquitous in real-world applications. Therefore, our experiments were performed in viscous and viscoelastic media, which are typical environments for synthetic and biological processes on the microscale. Despite marked differences between the protocols in both fluids, we find that the optimal control protocol and the corresponding average particle trajectory always obey a time-reversal symmetry. We show that this symmetry, which surprisingly applies here to a class of processes far from thermal equilibrium, holds universally for various systems, including active, granular, and long-range correlated media in their linear regimes. The uncovered symmetry provides a rigorous and versatile criterion for optimal control that greatly facilitates the search for energy-efficient transport strategies in a wide range of systems. Using a machine learning algorithm, we demonstrate that the algorithmic exploitation of time-reversal symmetry can significantly enhance the performance of numerical optimization algorithms.