Yawata Koichiro, Fukami Kai, Taira Kunihiko, Nakao Hiroya
Department of Systems and Control Engineering, Tokyo Institute of Technology, Tokyo 152-8552, Japan.
Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, Los Angeles, California 90095, USA.
Chaos. 2024 Jun 1;34(6). doi: 10.1063/5.0205718.
We present a phase autoencoder that encodes the asymptotic phase of a limit-cycle oscillator, a fundamental quantity characterizing its synchronization dynamics. This autoencoder is trained in such a way that its latent variables directly represent the asymptotic phase of the oscillator. The trained autoencoder can perform two functions without relying on the mathematical model of the oscillator: first, it can evaluate the asymptotic phase and the phase sensitivity function of the oscillator; second, it can reconstruct the oscillator state on the limit cycle in the original space from the phase value as an input. Using several examples of limit-cycle oscillators, we demonstrate that the asymptotic phase and the phase sensitivity function can be estimated only from time-series data by the trained autoencoder. We also present a simple method for globally synchronizing two oscillators as an application of the trained autoencoder.
我们提出了一种相位自动编码器，它对极限环振荡器的渐近相位进行编码，这是一个表征其同步动力学的基本量。这种自动编码器的训练方式使得其潜在变量直接代表振荡器的渐近相位。经过训练的自动编码器无需依赖振荡器的数学模型即可执行两项功能：第一，它可以评估振荡器的渐近相位和相位灵敏度函数；第二，它可以根据作为输入的相位值在原始空间中重建极限环上的振荡器状态。通过几个极限环振荡器的例子，我们证明了经过训练的自动编码器仅从时间序列数据就可以估计渐近相位和相位灵敏度函数。我们还提出了一种简单的方法，作为经过训练的自动编码器的应用，用于使两个振荡器全局同步。
