FlowRefiner: Flow Matching-Based Iterative Refinement for 3D Turbulent Flow Simulation

TL;DR

FlowRefiner introduces a deterministic, flow matching-based iterative refinement framework for 3D turbulent flow simulation, achieving state-of-the-art accuracy and physical consistency in complex turbulence modeling.

Contribution

It replaces stochastic denoising with ODE-based correction and introduces a decoupled sigma schedule for stable, effective refinement.

Findings

Achieves state-of-the-art autoregressive prediction accuracy.

Demonstrates strong physical consistency in large-scale turbulence.

Applicable broadly to scientific iterative refinement problems.

Abstract

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.