FourierFlow: Frequency-aware Flow Matching for Generative Turbulence Modeling

Haixin Wang, Jia-Shu Pan, Hao Wu, Fan Zhang, Tailin Wu

Keywords: AI for PDE

Abstract:

Modeling turbulence governed by partial differential equations (PDEs) remains a central challenge in science and engineering. While diffusion-based generative models have recently shown promise for flow generation, we provide empirical and theoretical evidence that they suffer from severe spectral bias and common-mode noise, limiting high-fidelity synthesis.
We introduce FourierFlow, a frequency-aware generative framework that jointly mitigates these issues through three innovations: (i) a dual-branch backbone with a salient-flow attention branch capturing local–global dynamics; (ii) a frequency-guided Fourier mixing branch with adaptive fusion to explicitly counter spectral bias; and (iii) masked auto-encoder pre-training to implicitly emphasize high-frequency features. Across three canonical turbulent-flow benchmarks, FourierFlow achieves state-of-the-art accuracy, superior long-horizon stability, and robustness to noisy inputs, while generalizing well to out-of-distribution scenarios. Code is available at https://anonymous.4open.science/r/FourierFlow-847D.

Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)

Submission Number: 5465