One Scale at a Time: Scale-Autoregressive Modeling for Fluid Flow Distributions

• URL: http://arxiv.org/abs/2604.11403v1
• Date: Mon, 13 Apr 2026 12:44:04 GMT
• Title: One Scale at a Time: Scale-Autoregressive Modeling for Fluid Flow Distributions
• Abstract summary: We introduce scale-autoregressive modeling (SAR) for sampling flows on unstructured meshes hierarchically from coarse to fine.<n>It attains substantially lower distributional error and higher per-sample accuracy than state-of-the-art diffusion models.
• Score: 26.06889184077997
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Analyzing unsteady fluid flows often requires access to the full distribution of possible temporal states, yet conventional PDE solvers are computationally prohibitive and learned time-stepping surrogates quickly accumulate error over long rollouts. Generative models avoid compounding error by sampling states independently, but diffusion and flow-matching methods, while accurate, are limited by the cost of many evaluations over the entire mesh. We introduce scale-autoregressive modeling (SAR) for sampling flows on unstructured meshes hierarchically from coarse to fine: it first generates a low-resolution field, then refines it by progressively sampling higher resolutions conditioned on coarser predictions. This coarse-to-fine factorization improves efficiency by concentrating computation at coarser scales, where uncertainty is greatest, while requiring fewer steps at finer scales. Across unsteady-flow benchmarks of varying complexity, SAR attains substantially lower distributional error and higher per-sample accuracy than state-of-the-art diffusion models based on multi-scale GNNs, while matching or surpassing a flow-matching Transolver (a linear-time transformer) yet running 2-7x faster than this depending on the task. Overall, SAR provides a practical tool for fast and accurate estimation of statistical flow quantities (e.g., turbulent kinetic energy and two-point correlations) in real-world settings.

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