Bayesian framework for simulation of dynamical systems from multidimensional data using recurrent neural network

Area of Science:

• Dynamical systems theory
• Machine learning
• Atmospheric science

Background:

• Dynamical models are crucial for understanding complex systems.
• Extracting meaningful dynamics from noisy, high-dimensional time series data remains a challenge.
• Existing methods often struggle with joint reconstruction of embeddings and evolution operators.

Purpose of the Study:

• To propose a novel data-driven method for building dynamical models from multidimensional time series.
• To develop a recurrent neural network architecture capable of joint embedding and evolution operator reconstruction.
• To validate the method on both synthetic and real-world atmospheric data.

Main Methods:

• Utilizing a specifically structured recurrent neural network for joint reconstruction.
• Employing Bayesian optimization for model structure and data-generating law hypothesis.
• Constructing a cost function for model learning based on Bayesian optimization.
• Testing the method on noisy, low-dimensional dynamical systems and a high-dimensional atmospheric model.

Main Results:

• Successfully reconstructed low-dimensional dynamical components and evolution operators from noisy data.
• Developed a data-driven model for the low-frequency variability (LFV) of Earth's midlatitude atmosphere using a quasigeostrophic model.
• Demonstrated accurate reproduction of key atmospheric LFV regimes in simulations.

Conclusions:

• The proposed recurrent neural network method offers a robust approach for data-driven dynamical modeling.
• The technique effectively handles noisy, high-dimensional data, including complex atmospheric systems.
• This method advances the ability to model and understand complex dynamical phenomena from observational data.