FourierFlow: Frequency-aware Flow Matching for Generative Turbulence Modeling
This work addresses the challenge of high-fidelity turbulent flow generation for science and engineering applications, representing an incremental improvement with novel architectural innovations.
The paper tackles the problem of generative turbulence modeling by addressing spectral bias and common-mode noise in diffusion-based models, proposing FourierFlow which demonstrates superior performance on three canonical turbulent flow scenarios with strong generalization capabilities.
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.