Rectified Flows for Fast Multiscale Fluid Flow Modeling

2025-06-03

AI Summary

Multi-scale fluid flow modeling suffers from high sensitivity to initial conditions, excessive inference steps (≥128) in existing conditional diffusion models, and prohibitive computational cost. To address these challenges, we propose a deterministic ODE sampling framework based on corrected flows—introducing Flow Matching to fluid statistical modeling for the first time. Our method learns a time-dependent velocity field and approximates optimal transport trajectories with straight-line paths, enabling efficient mapping from an input distribution to the target fluid field distribution. Evaluated on multi-scale fluid benchmarks, our approach achieves fidelity comparable to diffusion models using only eight ODE solver steps, significantly improving reconstruction quality of critical fine-scale structures—such as small vortices—while accelerating inference by over 15× and enabling high-resolution, real-time fluid field generation.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Learning with Manifolds

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

The statistical modeling of fluid flows is very challenging due to their multiscale dynamics and extreme sensitivity to initial conditions. While recently proposed conditional diffusion models achieve high fidelity, they typically require hundreds of stochastic sampling steps at inference. We introduce a rectified flow framework that learns a time-dependent velocity field, transporting input to output distributions along nearly straight trajectories. By casting sampling as solving an ordinary differential equation (ODE) along this straighter flow field, our method makes each integration step much more effective, using as few as eight steps versus (more than) 128 steps in standard score-based diffusion, without sacrificing predictive fidelity. Experiments on challenging multiscale flow benchmarks show that rectified flows recover the same posterior distributions as diffusion models, preserve fine-scale features that MSE-trained baselines miss, and deliver high-resolution samples in a fraction of inference time.

Problem

• Modeling multiscale fluid flows with high fidelity
• Reducing inference steps in fluid flow simulation
• Preserving fine-scale features in fast simulations

Innovation

• Rectified flow framework learns velocity field
• Uses ODE for straighter flow trajectories
• Achieves high fidelity with few steps