将神经算子与扩散模型集成可改进湍流建模中的谱表示
Integrating Neural Operators with Diffusion Models Improves Spectral Representation in Turbulence Modeling
AI总结：
该研究集成神经算子与扩散模型以解决湍流替代建模中神经算子的谱局限性，通过以神经算子为条件增强湍流结构分辨率，在多数据集上验证并显著提升能谱预测准确性，稳定长期预测并建立新范式。
摘要：
我们将神经算子与扩散模型集成，以解决湍流流动替代建模中神经算子的谱局限性。虽然神经算子具有计算效率，但它们在捕捉高频流动动力学方面存在不足，导致近似过于平滑。为克服这一问题，我们将扩散模型以神经算子为条件，以提高湍流结构的分辨率。我们的方法在不同数据集上对不同神经算子进行了验证，包括高雷诺数射流模拟和实验纹影测速。与单独使用神经算子相比，所提方法显著提高了预测能谱与真实分布的一致性。这使扩散模型能够通过扩散校正的自回归滚动稳定更长时间的预测，正如我们在本工作中所展示的。此外，本征正交分解分析证明了时空谱保真度的增强。这项工作建立了一种将生成模型与神经算子相结合的新范式，以推进湍流系统的替代建模，它还可用于涉及微观结构和高频内容的其他科学应用。详见我们的项目页面：vivekoommen.github.io/NO_DM
英文摘要：
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
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
