FlowRefiner: Flow Matching-Based Iterative Refinement for 3D Turbulent Flow Simulation
For neural PDE solvers, this work addresses the problem of error accumulation in autoregressive prediction of 3D turbulent flows, offering a deterministic refinement method that improves accuracy and physical consistency.
FlowRefiner introduces a flow matching-based iterative refinement framework for 3D turbulent flow simulation, achieving state-of-the-art autoregressive prediction accuracy and strong physical consistency on large-scale 3D turbulence.
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.