Simulating spatiotemporal turbulence with high fidelity remains a cornerstone challenge in computational fluid dynamics (CFD) due to its intricate multiscale nature and prohibitive computational demands. Traditional approaches typically employ closure models, which attempt to represent small-scale features in an unresolved manner. However, these methods often sacrifice accuracy and lose high-frequency/wavenumber information, especially in scenarios involving complex flow physics. In this paper, we introduce an innovative neural differentiable modeling framework designed to enhance the predictability and efficiency of spatiotemporal turbulence simulations. Our approach features differentiable hybrid modeling techniques that seamlessly integrate deep neural networks with numerical PDE solvers within a differentiable programming framework, synergizing deep learning with physics-based CFD modeling. Specifically, a hybrid differentiable neural solver is constructed on a coarser grid to capture large-scale turbulent phenomena, followed by the application of a Bayesian conditional diffusion model that generates small-scale turbulence conditioned on large-scale flow predictions. Two innovative hybrid architecture designs are studied, and their performance is evaluated through comparative analysis against conventional large eddy simulation techniques with physics-based subgrid-scale closures and purely data-driven neural solvers. The findings underscore the potential of the neural differentiable modeling framework to significantly enhance the accuracy and computational efficiency of turbulence simulations. This study not only demonstrates the efficacy of merging deep learning with physics-based numerical solvers but also sets a new precedent for advanced CFD modeling techniques, highlighting the transformative impact of differentiable programming in scientific computing.

中文翻译：

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基于扩散的超分辨率的二维时空湍流神经可微建模


由于其错综复杂的多尺度性质和令人望而却步的计算需求，以高保真度模拟时空湍流仍然是计算流体动力学 （CFD） 的一个基本挑战。传统方法通常采用闭包模型，该模型试图以未解析的方式表示小规模特征。然而，这些方法通常会牺牲精度并丢失高频/波数信息，尤其是在涉及复杂流动物理场的情况下。在本文中，我们介绍了一种创新的神经可微建模框架，旨在提高时空湍流模拟的可预测性和效率。我们的方法采用可微分混合建模技术，可在可微分编程框架内将深度神经网络与数值 PDE 求解器无缝集成，从而将深度学习与基于物理的 CFD 建模协同化。具体来说，在较粗的网格上构建了一个混合可微神经求解器来捕获大规模的湍流现象，然后应用贝叶斯条件扩散模型，该模型以大规模流动预测为条件生成小规模湍流。研究了两种创新的混合架构设计，并通过与具有基于物理的子网格尺度闭合和纯数据驱动的神经求解器的传统大涡模拟技术的比较分析来评估它们的性能。这些发现强调了神经可微建模框架在显著提高湍流模拟的准确性和计算效率方面的潜力。 这项研究不仅证明了将深度学习与基于物理的数值求解器相结合的有效性，还为高级 CFD 建模技术开创了新的先例，突出了可微分编程在科学计算中的变革性影响。