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

Multiscale dynamical systems characterized by interacting fast and slow processes are ubiquitous across scientific domains, from climate dynamics to fluid mechanics. Accurate modeling of such systems requires capturing both the long-term statistical properties governed by slow variables and the short-term transient dynamics driven by fast chaotic processes. We present a hybrid data-driven framework that integrates score-based generative modeling with Neural Ordinary Differential Equations (NODEs) to construct reduced-order models capable of reproducing both regimes. The slow component is represented by a score-based drift learned using denoising score matching, which provides the statistical closure needed to reproduce the invariant measure and short-lag correlations of the slow variables. The fast chaotic forcing is represented by a NODE trained on delay-embedded residuals extracted from observed trajectories. We validate this approach on a hierarchy of prototypical metastable systems driven by Lorenz 63 dynamics, including bistable potentials with additive and multiplicative forcing, tristable non-autonomous systems with cycloperiodic components, and a five-dimensional coupled slow-fast system in which the fast subsystem depends explicitly on the slow state. Our results demonstrate that the hybrid framework maintains statistical consistency over long time horizons while providing non-trivial short-horizon predictive skill for transition trajectories between metastable states. This skill is observed for lead times comparable to the Lyapunov time of the chaotic fast driver, which sets the intrinsic predictability horizon for pathwise forecasts. This work establishes a principled methodology for combining statistical closure techniques with explicit surrogate models of fast dynamics, offering a pathway toward predictive modeling of complex multiscale phenomena where both long-term statistics and short-term transients are essential.