  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.
