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

2026-04-18

AI Summary

Existing neural PDE solvers struggle to maintain high accuracy in autoregressive 3D turbulent flow prediction due to rapid accumulation of fine-scale errors. This work proposes an iterative optimization framework based on flow matching, which replaces stochastic denoising with a deterministic ODE correction mechanism, introduces a unified regression objective for velocity fields, and employs a decoupled sigma schedule independent of refinement depth to significantly enhance stability and precision in low-noise regimes. The method achieves state-of-the-art predictive performance on large-scale, multiscale 3D turbulence simulations while demonstrating excellent physical consistency.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Deep Generative Models & Autoencoders

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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.

Problem

• 3D turbulent flow
• autoregressive prediction
• neural PDE solvers
• error accumulation
• fine-scale structures

Innovation

• flow matching
• iterative refinement
• ODE-based correction
• sigma schedule
• turbulent flow simulation