Prediction of chaotic dynamics from data: An introduction

TL;DR

This paper introduces a principled method for predicting chaotic systems from data, combining dynamical systems theory with machine learning techniques like echo state and LSTM networks, supported by pedagogical examples and coding tutorials.

Contribution

It integrates chaos theory with machine learning approaches for time forecasting, providing a comprehensive, pedagogical introduction with practical coding resources.

Findings

Demonstrates prediction of chaotic systems like Lorenz using machine learning.

Provides pedagogical examples and tutorials for practical implementation.

Bridges dynamical systems theory with modern data-driven forecasting methods.

Abstract

This chapter offers a principled approach to the prediction of chaotic systems from data. First, we introduce some concepts from dynamical systems' theory and chaos theory. Second, we introduce machine learning approaches for time-forecasting chaotic dynamics, such as echo state networks and long-short-term memory networks, whilst keeping a dynamical systems' perspective. Third, the lecture contains informal interpretations and pedagogical examples with prototypical chaotic systems (e.g., the Lorenz system), which elucidate the theory. The chapter is complemented by coding tutorials (online) at https://github.com/MagriLab/Tutorials.