Xiao Rui, Kong Ling-Wei, Sun Zhong-Kui, Lai Ying-Cheng
School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, Arizona 85287, USA.
Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710129, China.
Phys Rev E. 2021 Jul;104(1-1):014205. doi: 10.1103/PhysRevE.104.014205.
In nonlinear dynamics, a parameter drift can lead to a sudden and complete cessation of the oscillations of the state variables-the phenomenon of amplitude death. The underlying bifurcation is one at which the system settles into a steady state from chaotic or regular oscillations. As the normal functioning of many physical, biological, and physiological systems hinges on oscillations, amplitude death is undesired. To predict amplitude death in advance of its occurrence based solely on oscillatory time series collected while the system still functions normally is a challenge problem. We exploit machine learning to meet this challenge. In particular, we develop the scheme of "parameter-aware" reservoir computing, where training is conducted for a small number of bifurcation parameter values in the oscillatory regime to enable prediction upon a parameter drift into the regime of amplitude death. We demonstrate successful prediction of amplitude death for three prototypical dynamical systems in which the transition to death is preceded by either chaotic or regular oscillations. Because of the completely data-driven nature of the prediction framework, potential applications to real-world systems can be anticipated.
在非线性动力学中，参数漂移可能导致状态变量的振荡突然完全停止，即振幅死亡现象。潜在的分岔是系统从混沌或规则振荡进入稳态的分岔。由于许多物理、生物和生理系统的正常功能依赖于振荡，振幅死亡是不希望出现的。仅根据系统仍正常运行时收集的振荡时间序列提前预测振幅死亡是一个具有挑战性的问题。我们利用机器学习来应对这一挑战。特别是，我们开发了“参数感知”水库计算方案，在振荡区域针对少量分岔参数值进行训练，以便在参数漂移到振幅死亡区域时进行预测。我们证明了对于三个典型动力学系统成功预测了振幅死亡，在这些系统中，向死亡的转变之前是混沌或规则振荡。由于预测框架完全是数据驱动的，因此可以预期其在实际系统中的潜在应用。
