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

TL;DR

This paper introduces an unsupervised reservoir computing method to predict unobserved bifurcations in nonlinear, non-stationary systems by extracting slowly varying parameters from time series data, enabling better understanding of qualitative system changes.

Contribution

It proposes a novel reservoir computing architecture with slow and fast reservoirs to extract and utilize slow parameter variations for bifurcation prediction without prior parameter knowledge.

Findings

Successfully predicts bifurcations in chaotic systems.

Demonstrates applicability to real-world fields like neuroscience and weather forecasting.

Shows ability to identify unobserved bifurcations from data.

Abstract

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.