用物理约束的生成模型加速湍流模拟，更准更稳。
Physics-aware generative models for turbulent fluid flows through energy-consistent stochastic interpolants
- 设计可学习参数的随机插值器，嵌入能量守恒与无散性
- 在柯尔莫戈洛夫流动上实现比现有方法更高的精度和稳定性
- 适合需要长期稳定模拟的流体力学研究者
生成模型在文本、图像和视频合成等领域已取得显著成功。本文探索其在流体动力学中的应用，特别是湍流模拟，传统数值求解器计算成本高昂。我们提出一种基于随机插值器的新颖随机生成模型，可在概率预测中融入能量稳定性与无散性等物理约束。不同于通常忽略物理规律的生成模型，本方法通过使随机插值器的参数为可学习系数，实现能量一致性。我们在基准湍流问题——柯尔莫戈洛夫流动上评估该方法，结果表明其在准确性和稳定性上均优于当前最优的自回归条件扩散模型（ACDMs）和PDE-Refiner。此外，相比标准随机插值器，本方法能实现更长时间滚动预测的稳定结果。结果表明，物理感知生成模型有望在加速并提升湍流模拟的同时，保持基本守恒性质。
原文摘要 · Abstract (English)
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.
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