# Predicting Critical Transitions in Multiscale Dynamical Systems Using Reservoir Computing

## TL;DR

This paper introduces a reservoir computing-based data-driven approach to predict rare critical transitions in multiscale nonlinear dynamical systems, demonstrating successful early predictions across various system dimensions.

## Contribution

The paper presents a novel application of reservoir computing for early prediction of critical transitions in slow-fast dynamical systems, highlighting its effectiveness and limitations.

## Key findings

- Predicts critical transitions several steps in advance
- Effective across low and high dimensional systems
- Highlights limitations in certain scenarios

## Abstract

We study the problem of predicting rare critical transition events for a class of slow-fast nonlinear dynamical systems. The state of the system of interest is described by a slow process, whereas a faster process drives its evolution and induces critical transitions. By taking advantage of recent advances in reservoir computing, we present a data-driven method to predict the future evolution of the state. We show that our method is capable of predicting a critical transition event at least several numerical time steps in advance. We demonstrate the success as well as the limitations of our method using numerical experiments on three examples of systems, ranging from low dimensional to high dimensional. We discuss the mathematical and broader implications of our results.