Rectified Flows for Fast Multiscale Fluid Flow Modeling

Understand

Statistical surrogate modeling of fluid flows is hard because dynamics are multiscale and highly sensitive to initial conditions.

• Conditional diffusion surrogates can be accurate, but usually need hundreds of stochastic sampling steps.
• We propose a rectified-flow surrogate that learns a time-dependent conditional velocity field transporting input-to-output laws along near-straight trajectories.
• Inference is then a deterministic ODE solve, making each function evaluation more informative: on multiscale 2D benchmarks, we match diffusion-class posterior statistics with only (8) ODE steps versus (\ge 128) for score-based diffusion.