FourierFlow: Frequency-aware Flow Matching for Generative Turbulence Modeling

• URL: http://arxiv.org/abs/2506.00862v1
• Date: Sun, 01 Jun 2025 06:59:27 GMT
• Title: FourierFlow: Frequency-aware Flow Matching for Generative Turbulence Modeling
• Authors: Haixin Wang, Jiashu Pan, Hao Wu, Fan Zhang, Tailin Wu,
• Abstract summary: We propose a novel generative turbulence modeling framework that enhances the frequency-aware learning by implicitly and explicitly mitigating spectral bias and common-mode noise.<n>FourierFlow comprises three key innovations. Firstly, we adopt a dual-branch backbone architecture, consisting of a salient flow attention branch with local-global awareness to focus on sensitive turbulence areas.<n>Thirdly, we leverage the high-frequency modeling capabilities of the masked auto-encoder pre-training and implicitly align the features of the generative model toward high-frequency components.
• Score: 10.73187148812722
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Modeling complex fluid systems, especially turbulence governed by partial differential equations (PDEs), remains a fundamental challenge in science and engineering. Recently, diffusion-based generative models have gained attention as a powerful approach for these tasks, owing to their capacity to capture long-range dependencies and recover hierarchical structures. However, we present both empirical and theoretical evidence showing that generative models struggle with significant spectral bias and common-mode noise when generating high-fidelity turbulent flows. Here we propose FourierFlow, a novel generative turbulence modeling framework that enhances the frequency-aware learning by both implicitly and explicitly mitigating spectral bias and common-mode noise. FourierFlow comprises three key innovations. Firstly, we adopt a dual-branch backbone architecture, consisting of a salient flow attention branch with local-global awareness to focus on sensitive turbulence areas. Secondly, we introduce a frequency-guided Fourier mixing branch, which is integrated via an adaptive fusion strategy to explicitly mitigate spectral bias in the generative model. Thirdly, we leverage the high-frequency modeling capabilities of the masked auto-encoder pre-training and implicitly align the features of the generative model toward high-frequency components. We validate the effectiveness of FourierFlow on three canonical turbulent flow scenarios, demonstrating superior performance compared to state-of-the-art methods. Furthermore, we show that our model exhibits strong generalization capabilities in challenging settings such as out-of-distribution domains, long-term temporal extrapolation, and robustness to noisy inputs. The code can be found at https://github.com/AI4Science-WestlakeU/FourierFlow.

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