Multilayer Perceptron Network Optimization for Chaotic Time Series Modeling.

Area of Science:

• Complex Systems Science
• Computational Neuroscience
• Data Science

Background:

• Chaotic time series exhibit inherent randomness and nonlinearity, posing significant challenges for accurate intermediate and long-term prediction.
• Multi-layer Perceptron (MLP) networks offer a robust framework for modeling complex, nonlinear dynamics found in chaotic systems.

Purpose of the Study:

• To develop an optimized framework for chaotic time series analysis using Multi-layer Perceptron (MLP) networks.
• To enhance the precision of chaotic time series prediction through a novel approximation method and information criterion.

Main Methods:

• A generalized degree of freedom approximation method for MLP networks was developed.
• The Akachi information criterion was derived and implemented as a loss function for model training.
• The framework integrated phase space reconstruction, model training, and model selection for chaotic time series.

Main Results:

• The proposed optimized MLP method demonstrated effectiveness in selecting the best model from candidate models.
• Numerical applications to both artificial and real-world chaotic time series validated the method's performance.
• The optimized models achieved high accuracy in multi-step prediction tasks.

Conclusions:

• The developed framework provides an effective approach for chaotic time series modeling and prediction.
• The generalized degree of freedom approximation and Akachi information criterion enhance MLP's capability in handling chaotic dynamics.
• This research offers a significant advancement in accurately predicting complex, unpredictable time series data.