Learning latent dynamics for partially observed chaotic systems.

Area of Science:

• Dynamical Systems and Control Theory
• Machine Learning for Scientific Discovery
• Data-Driven Modeling

Background:

• Partially observed dynamical systems pose challenges for traditional data-driven methods.
• Existing approaches often rely on delay embeddings and linear decompositions.
• Accurate forecasting and understanding long-term behavior are critical.

Purpose of the Study:

• To develop a data-driven framework for identifying latent representations of partially observed dynamical systems.
• To enhance forecasting accuracy and analyze long-term asymptotic patterns.
• To introduce a neural-network-based approach for augmented state-space modeling.

Main Methods:

• Utilizing a neural-network-based representation for an augmented state-space model.
• Jointly reconstructing latent states and learning ordinary differential equations in the latent space.
• Comparing the proposed framework against state-of-the-art methods using numerical experiments.

Main Results:

• The proposed framework demonstrates improved performance in short-term forecasting.
• It accurately captures long-term asymptotic patterns of the dynamical systems.
• Numerical experiments validate the framework's relevance and effectiveness.

Conclusions:

• The neural-network-based augmented state-space model offers a powerful approach for analyzing partially observed dynamical systems.
• This method advances data-driven identification for forecasting and understanding system dynamics.
• The framework provides insights into the relationship with Koopman operator theory and Takens' embedding theorem.