Incorporating coupling knowledge into echo state networks for learning spatiotemporally chaotic dynamics.

Area of Science:

• Complex Systems
• Machine Learning
• Dynamical Systems

Background:

• Machine learning (ML) shows promise for chaotic dynamical systems, enabling prediction and reconstruction.
• Purely data-driven ML struggles with large-scale chaotic systems due to model size and data requirements.

Purpose of the Study:

• To develop an efficient ML method for large-scale chaotic systems.
• To improve the performance and robustness of ML models by incorporating spatial coupling information.

Main Methods:

• Introduced physics-guided clustered echo state networks (ESNs).
• Leveraged the efficiency of ESNs and incorporated spatial coupling structure as an inductive bias.
• Tested on benchmark chaotic systems.

Main Results:

• Physics-informed ESNs outperformed existing ESN models in learning chaotic systems.
• Incorporating coupling knowledge enhanced model robustness to training and system variations.
• The model remained effective with imperfect or data-derived coupling knowledge.

Conclusions:

• Physics-guided clustered ESNs offer an efficient and robust approach for learning chaotic systems.
• Incorporating inductive biases like spatial coupling is beneficial for ML in complex systems.
• This physics-informed ML strategy has potential applications beyond ESNs.