用扩散模型提升神经算子对湍流高频结构的建模能力
Integrating Neural Operators with Diffusion Models Improves Spectral Representation in Turbulence Modeling
- 将扩散模型条件化于神经算子，增强湍流微结构分辨率
- 预测能量谱与真实分布对齐度显著提升，高雷诺数流动验证有效
- 适合需要高精度频域建模的科学仿真场景，如复杂流体系统
我们提出将神经算子与扩散模型结合，以解决其在湍流代理建模中对高频流动动态捕捉不足的问题。尽管神经算子具有计算效率优势，但其输出往往过于平滑，难以还原真实湍流的精细结构。为此，我们通过条件化扩散模型来修正神经算子的输出，显著提升了湍流结构的分辨率。该方法在多种神经算子和数据集上得到验证，包括高雷诺数喷流模拟及实验性施里伦速度测量数据。结果表明，所提方法显著改善了预测能量谱与真实分布的一致性。同时，基于本方法的扩散修正自回归滚动预测可实现更长时程的稳定预报。此外，本征正交分解分析显示空间-时间谱保真度显著增强。该工作为生成模型与神经算子融合提供了新范式，可推广至含微结构与高频成分的其他科学建模任务。
原文摘要 · Abstract (English)
We integrate neural operators with diffusion models to address the spectral limitations of neural operators in surrogate modeling of turbulent flows. While neural operators offer computational efficiency, they exhibit deficiencies in capturing high-frequency flow dynamics, resulting in overly smooth approximations. To overcome this, we condition diffusion models on neural operators to enhance the resolution of turbulent structures. Our approach is validated for different neural operators on diverse datasets, including a high Reynolds number jet flow simulation and experimental Schlieren velocimetry. The proposed method significantly improves the alignment of predicted energy spectra with true distributions compared to neural operators alone. This enables the diffusion models to stabilize longer forecasts through diffusion-corrected autoregressive rollouts, as we demonstrate in this work. Additionally, proper orthogonal decomposition analysis demonstrates enhanced spectral fidelity in space-time. This work establishes a new paradigm for combining generative models with neural operators to advance surrogate modeling of turbulent systems, and it can be used in other scientific applications that involve microstructure and high-frequency content. See our project page: vivekoommen.github.io/NO_DM
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