Integrating score-based generative modeling and neural ODEs for accurate representation of multiscale chaotic...

Area of Science:

• Computational physics and applied mathematics.
• Complex systems modeling.
• Data-driven scientific discovery.

Background:

• Multiscale dynamical systems with interacting fast and slow processes are common in climate dynamics and fluid mechanics.
• Accurate modeling requires capturing long-term statistical properties and short-term transient dynamics.
• Existing models often struggle to reproduce both statistical consistency and transient behavior.

Purpose of the Study:

• To develop a hybrid data-driven framework for reduced-order modeling of multiscale systems.
• To integrate score-based generative modeling with Neural Ordinary Differential Equations (NODEs).
• To accurately reproduce both long-term statistical properties and short-term transient dynamics.

Main Methods:

• A hybrid framework combining score-based generative modeling and NODEs.
• Score-based drift learned via denoising score matching for slow variable statistics.
• NODE trained on delay-embedded residuals for fast chaotic forcing representation.

Main Results:

• The framework successfully models prototypical metastable systems, including Lorenz 63 dynamics.
• Maintained statistical consistency over long time horizons.
• Demonstrated non-trivial short-horizon predictive skill for transition trajectories.

Conclusions:

• The hybrid approach effectively combines statistical closure with explicit surrogate modeling of fast dynamics.
• Offers a pathway for predictive modeling of complex multiscale phenomena.
• Achieved predictive skill up to the Lyapunov time of the chaotic fast driver.