标题： 随机系统中时间延迟的推断 显示英文标题

标题： Inference of time delay in stochastic systems

摘要： 时间延迟在许多实验和现实情况中普遍存在。 通常不清楚时间延迟是否在观察到的现象中起着重要作用，如果起作用，实际的时间滞后有多长。 在分析和建模此类系统时，这将是有价值的知识。 迄今为止，还没有一种通用的方法可以推断时间延迟。 为了解决这个问题，我们提出了并演示了两种不同的方法，用于推断具有反馈延迟的过阻尼朗之万系统中的时间延迟。 在第一部分中，我们专注于基于位置数据的功率谱密度，并利用时间延迟的特征标志来推断延迟时间。 在极限情况下，我们将对非线性时间延迟反馈力的观测结果与线性系统的解析结果建立了直接关系。 在其他情况下，尽管不存在这种直接关系，特征标志仍然存在，并可以通过半自动方法来推断延迟时间。 此外，有时并不总是可行或希望长时间观察一个系统以推断依赖关系和参数。 因此，在第二部分中，我们首次提出了一种结合神经网络的探测方法，以推断延迟时间，这种方法只需要短时间的观测时间序列。 这些用于推断随机系统中时间延迟的方法可能成为在广泛的应用领域中深入了解延迟作用的有价值工具——从反馈控制下单个胶体粒子的行为到如 flocking 和 swarming 等涌现的集体现象。 显示英文摘要

摘要： Time delay is ubiquitous in many experimental and real-world situations. It is often unclear whether time delay plays a significant role in observed phenomena, and if it does, how long the time lag really is. This would be invaluable knowledge when analyzing and modeling such systems. Hitherto, no universal method is available by which the time delay can be inferred. To address this problem, we propose and demonstrate two different methods to infer time delay in overdamped Langevin systems with delayed feedback. In the first part, we focus on the power spectral density based on the positional data and use a characteristic signature of the time delay to infer the delay time. In limiting cases, we establish a direct relation of the observations made for nonlinear time-delayed feedback forces to analytical results obtained for the linear system. In other situations despite the absence of this direct relation, the characteristic signature remains and can be exploited by a semiautomatic method to infer the delay time. Furthermore, it may not always desirable or possible to observe a system for a long time to infer dependencies and parameters. Thus, in the second part, we propose for the first time a probing method combined with a neural network to infer the delay time, which requires only short observation time series. These proposed methods for inferring time delays in stochastic systems may prove to be valuable tools for gaining deeper insight into the role of delay across a wide range of applications -- from the behavior of individual colloidal particles under feedback control to emergent collective phenomena such as flocking and swarming.