Comparative Analysis of Predicting Subsequent Steps in H\'enon Map

TL;DR

This study compares various machine learning models for predicting the chaotic Hénon map's future states, finding LSTM networks outperform others, especially over longer horizons and larger datasets.

Contribution

It provides a comprehensive evaluation of machine learning techniques for predicting chaotic systems, highlighting LSTM's superior performance in this context.

Findings

LSTM outperforms other models in prediction accuracy.

LSTM shows advantages for longer prediction horizons.

Model performance depends on dataset size and choice.

Abstract

This paper explores the prediction of subsequent steps in H\'enon Map using various machine learning techniques. The H\'enon map, well known for its chaotic behaviour, finds applications in various fields including cryptography, image encryption, and pattern recognition. Machine learning methods, particularly deep learning, are increasingly essential for understanding and predicting chaotic phenomena. This study evaluates the performance of different machine learning models including Random Forest, Recurrent Neural Network (RNN), Long Short-Term Memory (LSTM) networks, Support Vector Machines (SVM), and Feed Forward Neural Networks (FNN) in predicting the evolution of the H\'enon map. Results indicate that LSTM network demonstrate superior predictive accuracy, particularly in extreme event prediction. Furthermore, a comparison between LSTM and FNN models reveals the LSTM's advantage, especially for longer prediction horizons and larger datasets. This research underscores the significance of machine learning in elucidating chaotic dynamics and highlights the importance of model selection and dataset size in forecasting subsequent steps in chaotic systems.