Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks

Area of Science:

• Complex Systems Science
• Machine Learning
• Dynamical Systems Theory

Background:

• High-dimensional chaotic systems present significant forecasting challenges due to their inherent complexity and sensitivity to initial conditions.
• Traditional forecasting methods often struggle with the nonlinear dynamics characteristic of these systems.
• Recurrent neural networks, particularly LSTMs, have emerged as powerful tools for modeling sequential data and complex dynamics.

Purpose of the Study:

• To introduce and evaluate a novel data-driven forecasting method for high-dimensional chaotic systems.
• To assess the performance of long short-term memory (LSTM) recurrent neural networks against Gaussian processes (GPs) for time series forecasting.
• To develop a hybrid LSTM architecture for improved long-term forecasting accuracy and convergence to invariant measures.

Main Methods:

• Implementation of LSTM neural networks for inference in the reduced order space of high-dimensional dynamical systems.
• Comparative analysis of LSTM performance against Gaussian processes using time series data from the Lorenz 96 system, Kuramoto-Sivashinsky equation, and a climate model.
• Development of a hybrid Mean Stochastic Model-LSTM (MSM-LSTM) architecture to enhance convergence properties.

Main Results:

• LSTM networks demonstrated superior short-term forecasting accuracy compared to Gaussian processes across all tested chaotic systems.
• The proposed LSTM models effectively captured the nonlinear dynamics and attractor of the chaotic systems.
• The hybrid MSM-LSTM architecture showed promise in ensuring convergence to the invariant measure, extending forecasting capabilities.

Conclusions:

• Data-driven LSTM networks offer a robust and effective approach for forecasting high-dimensional chaotic systems.
• The hybrid MSM-LSTM method provides a significant advancement for accurate and stable long-term predictions in complex dynamical systems.
• This study highlights the potential of advanced machine learning techniques in advancing scientific forecasting capabilities.