关键词: 动力学引导扩散模型, Kolmogorov湍流, 机器学习

Abstract: Accurate prediction of turbulence evolution is crucial for understanding turbulence. Existing machine learning-based turbulence research largely focuses on predicting the statistical behavior of turbulence after it reaches statistical steady state, failing to characterize the entire evolutionary process from the initial state to statistical steady state. To address this issue, this study proposes a dynamic guided diffusion model (DYffusion) to predict the entire evolution of Kolmogorov turbulence from its initial distribution to statistical steady state, and compares it with methods such as Markov Neural Operator (MNO) and U-Net trained using a teacher-forced approach. The results show that, compared to MNO and U-Net, DYffusion can not only accurately reproduce the evolutionary process of Kolmogorov turbulence but also accurately predict the final statistical steady-state distribution.

Key words: Dynamics-informed Diffusion Models, Kolmogorov Turbulence, Machine Learning