Learning dynamical systems in noise using convolutional neural networks

Area of Science:

• Complex systems analysis
• Nonlinear dynamics and chaos theory
• Time series analysis and signal processing

Background:

• Distinguishing deterministic chaos from stochastic dynamics is difficult due to unavoidable noise contamination.
• Noise-corrupted chaotic dynamics can closely resemble random processes, complicating analysis.
• Traditional methods struggle when state variables are unobserved.

Purpose of the Study:

• To develop a novel approach for classifying noise-corrupted chaotic dynamics versus stochastic dynamics.
• To formulate the problem as a multi-class classification task using signal and image processing.
• To leverage deep learning for learning system dynamics from time series data.

Main Methods:

• Time series data transformed into textured images: spectrograms and unthresholded recurrence plots (UTRPs).
• A Convolutional Neural Network (CNN) designed to learn dynamics from joint image representations.
• Characterization of system dynamics using signal and image processing techniques.

Main Results:

• The CNN successfully learns system dynamics from the joint representation of UTRP and spectrogram images.
• The approach effectively distinguishes between deterministic chaotic and stochastic systems even with noise.
• Robustness and scalability demonstrated across various noise levels.

Conclusions:

• The proposed deep learning method offers a powerful pattern recognition solution for identifying chaotic dynamics in noisy time series.
• Combining UTRP and spectrogram representations enhances the learning of dynamical systems in the presence of colored noise.
• This method provides a robust framework for analyzing complex systems where state variables are not directly measured.