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.

翻译：分析非稳态流体流通常需要访问可能的时间状态的完整分布，然而传统PDE求解器计算成本过高，且基于学习的时间步进代理会在长时间推进中迅速累积误差。生成模型通过独立采样状态避免误差累积，但扩散和流匹配方法虽然精确，却受限于对整个网格进行多次评估的成本。我们提出尺度自回归建模（SAR），用于在非结构化网格上从粗到细分层采样流场：首先生成低分辨率场，然后通过逐步采样更高分辨率（以粗尺度预测为条件）进行细化。这种从粗到细的分解通过将计算集中在不确定性最大的粗尺度上，同时减少细尺度上的步骤，从而提高了效率。在多个不同复杂度的非稳态流基准测试中，SAR比基于多尺度GNN的最先进扩散模型实现了更低分布误差和更高的逐样本精度，同时匹配或超越流匹配Transolver（一种线性时间变换器），且根据任务不同运行速度快2-7倍。总体而言，SAR为实际场景中快速准确估计统计流场量（如湍流动能和两点相关性）提供了实用工具。