mlsanityData to 14 Oct 2026

Generative emulation of chaotic dynamics with coherent prior

arXiv 2504.14264 ↗First posted 19 Apr 2025cs.LG stat.MLcited by 7

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Abstract (arXiv)

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.

Key facts. Cited by 7 papers in the map (data through 14 Oct 2026). Builds on 44 of its 76 references that are in the map. First posted on arXiv 19 Apr 2025.

Builds on

44 of 76 references.

References · 44

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32 more
  1. 2022Message Passing Neural PDE Solverscited by 386
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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 3; 2026: 4.

7 papers.

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Close in wording, no citation either way

  1. 2025Physics-aware generative models for turbulent fluid flows through energy-consistent stochastic interpolants
  2. 2023Bayesian Conditional Diffusion Models for Versatile Spatiotemporal Turbulence Generation
  3. 2024Generative Learning of the Solution of Parametric Partial Differential Equations Using Guided Diffusion Models and Virtual Observations
  4. 2026Optimal-Transport-Guided Functional Flow Matching for Turbulent Field Generation in Hilbert Space
  5. 2025Lazy Diffusion: Mitigating spectral collapse in generative diffusion-based stable autoregressive emulation of turbulent flows
  6. 2026StocBench: A Benchmark for Generative Modeling of Stochastic Dynamics
  7. 2025Learning Temporally Consistent Turbulence Between Sparse Snapshots via Diffusion Models
  8. 2025Fast and Flexible Probabilistic Forecasting of Dynamical Systems using Flow Matching and Physical Perturbation