Hybrid forecasting of chaotic processes: Using machine learning in conjunction with a knowledge-based model.

Area of Science:

• Dynamical Systems Theory
• Machine Learning
• Computational Science

Background:

• Model-based forecasting of chaotic systems relies on mechanistic knowledge, often incomplete.
• Machine learning excels at forecasting from time series data without prior system knowledge.
• Existing knowledge-based models face limitations due to gaps in mechanistic understanding.

Purpose of the Study:

• To develop a hybrid forecasting method integrating knowledge-based models and machine learning.
• To enhance the accuracy and prediction horizon of chaotic system forecasting.
• To leverage machine learning to augment incomplete mechanistic models.

Main Methods:

• A general hybrid forecasting scheme combining a knowledge-based model with a machine learning technique.
• Utilizing reservoir computing as the machine learning component.
• Testing the hybrid approach on low-dimensional and high-dimensional spatiotemporal chaotic systems.

Main Results:

• The hybrid forecasting technique demonstrated significantly improved prediction accuracy.
• The combined approach achieved a longer prediction period than either component alone.
• Successful application to both simple and complex chaotic systems.

Conclusions:

• Hybrid forecasting effectively bridges mechanistic knowledge gaps in dynamical systems.
• Combining model-based and machine learning approaches offers superior forecasting capabilities.
• This method shows great promise for applications like weather forecasting.