Nonlinear and non-stationary processes are prevalent in various natural and physical phenomena, where system dynamics can change qualitatively due to bifurcation phenomena. Traditional machine learning methods have advanced our ability to learn and predict such systems from observed time series data. However, predicting the behavior of systems with temporal parameter variations without knowledge of true parameter values remains a significant challenge. This study leverages the reservoir computing framework to address this problem by unsupervised extraction of slowly varying system parameters from time series data. We propose a model architecture consisting of a slow reservoir with long timescale internal dynamics and a fast reservoir with short timescale dynamics. The slow reservoir extracts the temporal variation of system parameters, which are then used to predict unknown bifurcations in the fast dynamics. Through experiments using data generated from chaotic dynamical systems, we demonstrate the ability to predict bifurcations not present in the training data. Our approach shows potential for applications in fields such as neuroscience, material science, and weather prediction, where slow dynamics influencing qualitative changes are often unobservable.

使用水库计算框架从时间序列数据中无监督地提取系统的缓慢变化参数，进而预测快速动态中未知的分岔现象。

Prediction of Unobserved Bifurcation by Unsupervised Extraction of
  Slowly Time-Varying System Parameter Dynamics from Time Series Using
  Reservoir Computing

利用储层计算从时间序列中无监督提取缓慢变动系统参数动态预测未观测到的分叉