FourierFlow: Frequency-aware Flow Matching for Generative Turbulence Modeling

2025-06-01

AI Summary

To address the large spectral bias and strong common-mode noise in turbulence modeling using generative models, this paper proposes a frequency-aware flow-matching framework. Methodologically, it introduces a novel dual-branch architecture: a sensitive-flow attention branch captures local–global turbulent structures, while a Fourier-mixing branch explicitly corrects spectral deviations; additionally, masked autoencoding pretraining enhances high-frequency representation learning. The approach integrates frequency-domain analysis, flow matching, dual-branch attention, Fourier-space feature fusion, and PDE-constrained generation. Evaluated on three canonical turbulence benchmarks, the method significantly outperforms state-of-the-art (SOTA) methods. It demonstrates strong generalization capabilities—including out-of-distribution (OOD) domain adaptation, long-horizon extrapolation beyond 100 time steps, and over 40% improvement in noise robustness.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Natural Language Processing: Generation
• Computer Vision: Generative Adversarial Networks (GANs) for Vision

Application Category

• Social Networks and Social Media: Generative AI / large language models and their impact on social systems
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

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.

Problem

• Addresses spectral bias in generative turbulence modeling
• Mitigates common-mode noise in high-fidelity flow generation
• Enhances frequency-aware learning for turbulent systems

Innovation

• Dual-branch backbone with local-global attention
• Frequency-guided Fourier mixing branch
• Masked auto-encoder for high-frequency modeling