预测与机器学习的同步
Anticipating synchronization with machine learning
摘要：
在动态系统的应用中，可能会出现需要预测同步开始的情况，因为它可能导致系统性能和行为的特征和显著变化，无论是好是坏。在实验和实际环境中，系统方程往往是未知的，这就需要开发一个无模型和完全数据驱动的预测框架。我们认为这个具有挑战性的问题可以通过机器学习来解决。特别是，利用水库计算或回声状态网络，我们设计了一个“参数感知”的计划，训练神经机使用异步时间序列，即，在同步开始之前的参数范围内。经过适当训练的机器将拥有预测同步过渡的能力，因为在给定参数漂移量的情况下，可以准确地预测系统是保持异步还是表现出同步动态。我们展示了基于机器学习的框架，使用代表性的混沌模型和小型网络系统，表现出连续（二阶）或突然（一阶）的过渡。一个显著的特征是，对于同步呈现爆炸性（一阶）转变和滞后回线的网络系统，机器学习方案能够准确地预测这些特征，包括与前向和后向转变路径相关联的转变点的精确位置。
英文摘要：
In applications of dynamical systems, situations can arise where it is desired to predict the onset of synchronization as it can lead to characteristic and significant changes in the system performance and behaviors, for better or worse. In experimental and real settings, the system equations are often unknown, raising the need to develop a prediction framework that is model free and fully data driven. We contemplate that this challenging problem can be addressed with machine learning. In particular, exploiting reservoir computing or echo state networks, we devise a "parameter-aware" scheme to train the neural machine using asynchronous time series, i.e., in the parameter regime prior to the onset of synchronization. A properly trained machine will possess the power to predict the synchronization transition in that, with a given amount of parameter drift, whether the system would remain asynchronous or exhibit synchronous dynamics can be accurately anticipated. We demonstrate the machine-learning based framework using representative chaotic models and small network systems that exhibit continuous (second-order) or abrupt (first-order) transitions. A remarkable feature is that, for a network system exhibiting an explosive (first-order) transition and a hysteresis loop in synchronization, the machine learning scheme is capable of accurately predicting these features, including the precise locations of the transition points associated with the forward and backward transition paths.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
