Deep Learning for chaos detection.

Area of Science:

• Dynamical Systems and Chaos Theory
• Artificial Intelligence and Machine Learning

Background:

• Chaos detection is crucial for understanding complex dynamical systems.
• Traditional methods for chaos detection can be computationally intensive.

Purpose of the Study:

• To investigate the application of Deep Learning techniques for solving chaos detection problems.
• To evaluate the performance of different neural network architectures in classifying time series data from chaotic systems.

Main Methods:

• Utilized three artificial neural network architectures: Multi-layer Perceptron (MLP), Convolutional Neural Network (CNN), and Long Short-Term Memory (LSTM) cells.
• Trained neural networks on time series data generated from the Logistic map (discrete) and the Lorenz system (continuous).
• Classified time series data into 'regular' or 'chaotic' categories.

Main Results:

• Deep Learning models successfully classified time series data, distinguishing between regular and chaotic behaviors.
• The approach enabled efficient analysis of biparametric and triparametric regions within the Lorenz system.
• Demonstrated the potential of AI for low-cost, high-speed chaos analysis.

Conclusions:

• Deep Learning provides a powerful and computationally efficient tool for chaos detection in dynamical systems.
• Artificial neural networks can accurately identify chaotic dynamics from time series data.
• This methodology facilitates the exploration of complex parameter spaces in systems like the Lorenz attractor.