School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China.
School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China.
Chaos. 2021 Jan;31(1):011104. doi: 10.1063/5.0033870.
Can a neural network trained by the time series of system A be used to predict the evolution of system B? This problem, knowing as transfer learning in a broad sense, is of great importance in machine learning and data mining yet has not been addressed for chaotic systems. Here, we investigate transfer learning of chaotic systems from the perspective of synchronization-based state inference, in which a reservoir computer trained by chaotic system A is used to infer the unmeasured variables of chaotic system B, while A is different from B in either parameter or dynamics. It is found that if systems A and B are different in parameter, the reservoir computer can be well synchronized to system B. However, if systems A and B are different in dynamics, the reservoir computer fails to synchronize with system B in general. Knowledge transfer along a chain of coupled reservoir computers is also studied, and it is found that, although the reservoir computers are trained by different systems, the unmeasured variables of the driving system can be successfully inferred by the remote reservoir computer. Finally, by an experiment of chaotic pendulum, we demonstrate that the knowledge learned from the modeling system can be transferred and used to predict the evolution of the experimental system.
一个通过系统 A 的时间序列训练的神经网络能否用于预测系统 B 的演化？这个问题，广义上被称为迁移学习，在机器学习和数据挖掘中非常重要，但尚未针对混沌系统进行研究。在这里，我们从基于同步的状态推断的角度研究了混沌系统的迁移学习，其中通过训练混沌系统 A 的储层计算机用于推断混沌系统 B 的未测量变量，而 A 在参数或动力学方面与 B 不同。结果发现，如果系统 A 和 B 在参数上不同，则储层计算机可以很好地与系统 B 同步。然而，如果系统 A 和 B 在动力学上不同，则储层计算机通常无法与系统 B 同步。还研究了沿耦合储层计算机链的知识转移，结果发现，尽管储层计算机是通过不同的系统进行训练的，但可以通过远程储层计算机成功推断出驱动系统的未测量变量。最后，通过混沌摆实验，我们证明了从建模系统中学习到的知识可以被转移并用于预测实验系统的演化。
