Comparative Analysis of Predicting Subsequent Steps in Hénon Map
This work addresses the challenge of forecasting chaotic dynamics, which has applications in fields like cryptography and pattern recognition, but it is incremental as it applies existing methods to a known chaotic system.
This paper tackled the problem of predicting subsequent steps in the chaotic Hénon Map using various machine learning models, finding that LSTM networks demonstrated superior predictive accuracy, especially for longer prediction horizons and larger datasets.
This paper explores the prediction of subsequent steps in Hénon Map using various machine learning techniques. The Hénon 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 Hénon 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.