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

arXiv: https://arxiv.org/abs/2406.13995 · HTML: https://mlsanity.com/paper/2406.13995/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 42 references that are in the map.
- First posted on arXiv 20 Jun 2024.

## Builds on (most cited first, 5 of 5)

- [Machine learning prediction of critical transition and system collapse](https://mlsanity.com/paper/2012.01545/) (2020)
- [Reservoir Computing with Diverse Timescales for Prediction of Multiscale Dynamics](https://mlsanity.com/paper/2108.09446/) (2021)
- [Exploiting Multiple Timescales in Hierarchical Echo State Networks](https://mlsanity.com/paper/2101.04223/) (2021)
- [Dimension of Reservoir Computers](https://mlsanity.com/paper/1912.06472/) (2019)
- [Machine-learning parameter tracking with partial state observation](https://mlsanity.com/paper/2311.09142/) (2023)

## Abstract (arXiv)

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.