Generative emulation of chaotic dynamics with coherent prior

2025-04-19

AI Summary

To address pervasive skill degradation and physical inconsistency in long-term simulations of chaotic systems, this paper proposes Cohesion, a generative framework that uniquely leverages deep Koopman operator–learned stable long sequences—encoding large-scale coherent structures in turbulence—as priors to guide diffusion-based full-sequence conditional denoising. By reformulating forecasting as a trajectory planning task under explicit physical constraints, Cohesion abandons the autoregressive paradigm, enabling non-autoregressive, long-horizon consistent modeling. Evaluated on Kolmogorov flow, the shallow-water equations, and subseasonal-to-seasonal climate systems, Cohesion achieves substantial improvements in long-term forecast accuracy, supports efficient and physically consistent simulation from partial observations, and reduces computational cost by an order of magnitude compared to conventional methods.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Deep Generative Models & Autoencoders
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

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.

Problem

• Emulating chaotic dynamics with physically realistic outputs
• Improving generative simulation quality via coherent priors
• Enhancing long-range forecasting in partially-observed systems

Innovation

• Coherent prior-guided diffusion modeling for dynamics emulation
• Reduced-order models for efficient coherent structure approximation
• Trajectory planning reframing to minimize autoregressive costs