Cohesion: Coherence-Based Diffusion for Long-Range Dynamics Forecasting
Keywords: PDE, diffusion, dynamics, emulator
TL;DR: We reveal connections between turbulence and diffusion, using RL principles for faster inference than autoregressive diffusion, outperforming SoTAs on various difficult PDE tasks, extending the predictability range of dynamical system emulators.
Abstract: We recast existing works on probabilistic dynamics forecasting through a unified framework connecting turbulence and diffusion principles: Cohesion. Specifically, we relate the coherent part of nonlinear dynamics as a conditioning prior in a denoising process, which can be efficiently estimated using reduced-order models. This fast generation of long prior sequences allows us to reframe forecasting as trajectory planning, a common task in RL. This reformulation is beneficial because we can perform a single conditional denoising pass for an entire sequence, rather than autoregressively over long lead time, gaining orders-of-magnitude speedups with little performance loss. Nonetheless, Cohesion supports flexibility through temporal composition that allows iterations to be performed over smaller subsequences, with autoregressive being a special case. To ensure temporal consistency within and between subsequences, we incorporate a model-free, small receptive window via temporal convolution that leverages large NFEs during denoising. Finally, we perform our guidance in a classifier-free manner to handle a broad range of conditioning scenarios for zero-shot forecasts. Our experiments demonstrate that Cohesion outperforms state-of-the-art probabilistic emulators for chaotic systems over long lead time, including in Kolmogorov Flow and Shallow Water Equation. Its low spectral divergence highlights Cohesion's ability to resolve multi-scale physical structures, even in partially-observed cases, and are thus essential for long-range, high-fidelity, physically-realistic emulation.
Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)
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Submission Number: 10525
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