Convolutional autoencoder and conditional random fields hybrid for predicting spatial-temporal chaos.

Area of Science:

• Complex Systems Science
• Computational Physics
• Data Science

Background:

• Spatially-extended systems often exhibit chaotic dynamics, generating complex high-dimensional time series.
• Predicting the future evolution of these systems is challenging due to their inherent nonlinearity and sensitivity to initial conditions.

Purpose of the Study:

• To develop a data-driven approach for accurate prediction of high-dimensional chaotic time series.
• To leverage dimension reduction and probabilistic modeling for enhanced forecasting capabilities.

Main Methods:

• Utilized a convolutional autoencoder for effective dimension reduction and feature extraction from time series data.
• Employed a conditional random field operating in the reduced feature space for probabilistic prediction.
• Implemented a feedback loop with iterated predictions to forecast the system's future evolution.

Main Results:

• Demonstrated excellent performance in predicting chaotic time series.
• Successfully evaluated the method on Lorenz-96 systems and Kuramoto-Sivashinsky equations.
• Showcased the algorithm's ability to handle varying system sizes and complexities.

Conclusions:

• The proposed data-driven method offers a robust solution for predicting chaotic time series from spatially-extended systems.
• The combination of deep learning for feature extraction and probabilistic models for prediction is highly effective.
• This approach holds significant potential for applications in various scientific domains requiring time series forecasting.