Characterization of Fractal Basins Using Deep Convolutional Neural Networks

TL;DR

This paper introduces a deep learning approach to measure the fractal dimension of chaotic system basins, achieving comparable accuracy to traditional methods but with significantly faster computation.

Contribution

The authors develop a novel deep learning algorithm that accurately predicts fractal dimensions of chaotic basins, significantly improving computational efficiency.

Findings

Deep learning model predicts fractal dimensions with high accuracy.

Algorithm is approximately ten times faster than traditional methods.

Method applies to the Duffing oscillator across various parameters.

Abstract

Neural network models have recently demonstrated impressive prediction performance in complex systems where chaos and unpredictability appear. In spite of the research efforts carried out on predicting future trajectories or improving their accuracy compared to numerical methods, not sufficient work has been done by using deep learning techniques in which they characterize the unpredictability of chaotic systems or give a general view of the global unpredictability of a system. In this work we propose a novel approach based on deep learning techniques to measure the fractal dimension of the basins of attraction of the Duffing oscillator for a variety of parameters. As a consequence, we provide an algorithm capable of predicting fractal dimension measures as accurately as the conventional algorithm, but with a computation speed about ten times faster.