用确定性微分方程迭代修正3D湍流模拟，提升预测精度与物理一致性。
FlowRefiner: Flow Matching-Based Iterative Refinement for 3D Turbulent Flow Simulation
- 基于流匹配的确定性迭代修正，取代随机去噪。
- 在多尺度湍流数据上实现当前最优的自回归预测精度。
- 适用于科学建模中的各类迭代精修问题，尤其适合高精度模拟。
3D湍流的准确自回归预测对神经微分方程求解器仍是挑战，因小尺度结构的微小误差会随推演快速累积。本文提出FlowRefiner，一种基于流匹配的3D湍流模拟迭代精修框架。该方法以确定性常微分方程（ODE）修正替代随机去噪，所有精修阶段采用统一的速度场回归目标，并引入解耦的噪声调度机制，使噪声范围独立于精修深度。这些设计在小噪声环境下实现了稳定有效的精修。在具有丰富多尺度结构的大规模3D湍流实验中，FlowRefiner达到了当前最优的自回归预测精度和强物理一致性。尽管针对湍流模拟设计，该框架亦广泛适用于科学建模中的迭代精修问题。
原文摘要 · Abstract (English)
Accurate autoregressive prediction of 3D turbulent flows remains challenging for neural PDE solvers, as small errors in fine-scale structures can accumulate rapidly over rollout. In this paper, we propose FlowRefiner, a flow matching-based iterative refinement framework for 3D turbulent flow simulation. The method replaces stochastic denoising refinement with deterministic ODE-based correction, uses a unified velocity-field regression objective across all refinement stages, and introduces a decoupled sigma schedule that fixes the noise range independently of refinement depth. These design choices yield stable and effective refinement in the small-noise regime. Experiments on large-scale 3D turbulence with rich multi-scale structures show that FlowRefiner achieves state-of-the-art autoregressive prediction accuracy and strong physical consistency. Although developed for turbulent flow simulation, the proposed framework is broadly applicable to iterative refinement problems in scientific modeling.
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