Generative emulation of chaotic dynamics with coherent prior

TL;DR

Cohesion addresses the challenge of long-range, physically realistic emulation of chaotic dynamics by integrating turbulence-inspired coherent priors with diffusion-based generative modeling. It uses reduced-order models, notably deep Koopman operators, to provide fast, stable large-scale guidance and treats forecasting as trajectory planning to enable a single, global denoising pass over the horizon, aided by classifier-free guidance and temporal composition. Across Kolmogorov flow, shallow water dynamics, and subseasonal-to-seasonal climate regimes, Cohesion achieves superior long-range skill with physically consistent outputs and substantial speedups over autoregressive diffusion baselines, while showing robustness to incomplete priors. The framework offers a principled, turbulence-grounded path for data-driven emulation that can enhance uncertainty quantification and ensemble generation in geophysical forecasting, with potential extensions to coupled Earth-system components and alternative diffusion-as-closure approaches such as Schrödinger bridges or flow matching.

Abstract

Data-driven emulation of nonlinear dynamics is challenging due to long-range skill decay that often produces physically unrealistic outputs. Recent advances in generative modeling aim to address these issues by providing uncertainty quantification and correction. However, the quality of generated simulation remains heavily dependent on the choice of conditioning priors. In this work, we present an efficient generative framework for dynamics emulation, unifying principles of turbulence with diffusion-based modeling: Cohesion. Specifically, our method estimates large-scale coherent structure of the underlying dynamics as guidance during the denoising process, where small-scale fluctuation in the flow is then resolved. These coherent priors are efficiently approximated using reduced-order models, such as deep Koopman operators, that allow for rapid generation of long prior sequences while maintaining stability over extended forecasting horizon. With this gain, we can reframe forecasting as trajectory planning, a common task in reinforcement learning, where conditional denoising is performed once over entire sequences, minimizing the computational cost of autoregressive-based generative methods. Empirical evaluations on chaotic systems of increasing complexity, including Kolmogorov flow, shallow water equations, and subseasonal-to-seasonal climate dynamics, demonstrate Cohesion superior long-range forecasting skill that can efficiently generate physically-consistent simulations, even in the presence of partially-observed guidance.

Figures (25)

• Figure 1: Overview of Cohesion: an emulation framework integrating turbulence principles with diffusion-based modeling. A reduced-order model (ROM) emulates large-scale coherent flow, which serves as a conditioning prior in the generative, resolving process. Inspired by trajectory planning, Cohesion incorporates several key features to enhance flexibility and consistency, including: (a) classifier-free guidance for handling a broad range of conditioning scenarios -- e.g., using different coherent estimators in a "plug-and-play" manner; (b) temporal composition to accommodate variable-horizon sequences; and (c) model-free convolution to ensure global consistency.
• Figure 2: Qualitative single-member realization for Kolmogorov flow where Cohesion is physically-consistent and able to capture fine details over long rollouts compared to its probabilistic baselines.
• Figure 3: Quantitative ensemble result for Kolmogorov flow where Cohesion has the lowest RMSE ($\downarrow$; Equation \ref{['eq:rmse']}), MAE ($\downarrow$; Equation \ref{['eq:mae']}), and highest MS-SSIM ($\uparrow$; Equation \ref{['eq:ms-ssim']}) over long rollouts compared to its probabilistic baselines.
• Figure 4: Qualitative single-member realization for Shallow Water Equation where Cohesion is physically-consistent and able to capture fine details over long rollouts compared to its probabilistic baselines.
• Figure 5: Quantitative ensemble result for Shallow Water Equation where Cohesion has the lowest RMSE ($\downarrow$), MAE ($\downarrow$), and highest MS-SSIM ($\uparrow$) over long rollouts compared to its probabilistic baselines.