用生成式AI高效精准计算三维湍流统计量，比传统方法更真实。
Generative AI for fast and accurate statistical computation of fluids
- 基于条件得分扩散模型，端到端生成湍流数据。
- 生成样本高保真且谱分辨率优异，统计量误差小。
- 适合需要快速高精度流体模拟的科研与工程场景。
我们提出一种生成式AI算法GenCFD，用于解决三维湍流流动快速、准确且鲁棒的统计计算难题。该算法基于端到端的条件得分扩散模型，在一系列具有挑战性的流体问题上通过大量数值实验验证，可精准近似关键统计量，高效生成高质量、逼真的湍流样本，并保证出色的谱分辨率。相比之下，以最小化均方误差训练的确定性机器学习算法会退化为平均流。我们给出了严格的理论分析，揭示了扩散模型准确生成流体的意外机制，并通过可解析的简化模型展示了湍流中数学相关的特征。代码已公开于 https://github.com/camlab-ethz/GenCFD。
原文摘要 · Abstract (English)
We present a generative AI algorithm for addressing the pressing task of fast, accurate, and robust statistical computation of three-dimensional turbulent fluid flows. Our algorithm, termed as GenCFD, is based on an end-to-end conditional score-based diffusion model. Through extensive numerical experimentation with a set of challenging fluid flows, we demonstrate that GenCFD provides an accurate approximation of relevant statistical quantities of interest while also efficiently generating high-quality realistic samples of turbulent fluid flows and ensuring excellent spectral resolution. In contrast, ensembles of deterministic ML algorithms, trained to minimize mean square errors, regress to the mean flow. We present rigorous theoretical results uncovering the surprising mechanisms through which diffusion models accurately generate fluid flows. These mechanisms are illustrated with solvable toy models that exhibit the mathematically relevant features of turbulent fluid flows while being amenable to explicit analytical formulae. Our codes are publicly available at https://github.com/camlab-ethz/GenCFD.
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