标题： 具有物理意识的生成模型用于通过能量一致的随机插值器的湍流流体流动 显示英文标题

标题： Physics-aware generative models for turbulent fluid flows through energy-consistent stochastic interpolants

摘要： 生成模型在文本、图像和视频合成等领域展现了显著的成功。 在这项工作中，我们探索了生成模型在流体力学中的应用，特别是针对湍流模拟，因为经典的数值求解器计算成本高昂。 我们提出了一种基于随机插值的新颖随机生成模型，该模型能够在纳入物理约束（如能量稳定性和平行性）的同时实现概率预测。 与通常对底层物理定律不敏感的传统随机生成模型不同，我们的方法通过使随机插值的参数成为可学习的系数来嵌入能量一致性。 我们在一个基准湍流问题——科列莫可夫流（Kolmogorov flow）上评估了我们的方法，展示了优于最先进的替代方案（如自回归条件扩散模型（ACDMs）和PDE-Refiner）的优越准确性和稳定性。 此外，我们实现了比标准随机插值更长滚动时间范围内的稳定结果。 我们的结果突显了具备物理意识的生成模型在加速和增强湍流模拟方面以及在保持基本守恒属性方面的潜力。 显示英文摘要

摘要： Generative models have demonstrated remarkable success in domains such as text, image, and video synthesis. In this work, we explore the application of generative models to fluid dynamics, specifically for turbulence simulation, where classical numerical solvers are computationally expensive. We propose a novel stochastic generative model based on stochastic interpolants, which enables probabilistic forecasting while incorporating physical constraints such as energy stability and divergence-freeness. Unlike conventional stochastic generative models, which are often agnostic to underlying physical laws, our approach embeds energy consistency by making the parameters of the stochastic interpolant learnable coefficients. We evaluate our method on a benchmark turbulence problem - Kolmogorov flow - demonstrating superior accuracy and stability over state-of-the-art alternatives such as autoregressive conditional diffusion models (ACDMs) and PDE-Refiner. Furthermore, we achieve stable results for significantly longer roll-outs than standard stochastic interpolants. Our results highlight the potential of physics-aware generative models in accelerating and enhancing turbulence simulations while preserving fundamental conservation properties.