Lagrangian turbulence lies at the core of numerous applied and fundamental
problems related to the physics of dispersion and mixing in engineering,
bio-fluids, atmosphere, oceans, and astrophysics. Despite exceptional
theoretical, numerical, and experimental efforts conducted over the past thirty
years, no existing models are capable of faithfully reproducing statistical and
topological properties exhibited by particle trajectories in turbulence. We
propose a machine learning approach, based on a state-of-the-art Diffusion
Model, to generate single-particle trajectories in three-dimensional turbulence
at high Reynolds numbers, thereby bypassing the need for direct numerical
simulations or experiments to obtain reliable Lagrangian data. Our model
demonstrates the ability to quantitatively reproduce all relevant statistical
benchmarks over the entire range of time scales, including the presence of fat
tails distribution for the velocity increments, anomalous power law, and
enhancement of intermittency around the dissipative scale. The model exhibits
good generalizability for extreme events, achieving unprecedented intensity and
rarity. This paves the way for producing synthetic high-quality datasets for
pre-training various downstream applications of Lagrangian turbulence.

基于最先进的扩散模型的机器学习方法，能够生成具有高雷诺数的三维湍流中的单粒子轨迹，从而避免直接数值模拟或实验获得可靠的拉格朗日数据；该模型能够定量地重现整个时间尺度范围内的所有相关统计基准，包括速度增量的尾分布、异常幂律和耗散尺度周围间歇性的增强；该模型在极端事件方面表现出良好的普适性，实现了前所未有的强度和稀有性，为产生用于预训练拉格朗日湍流各种下游应用的合成高质量数据奠定了基础。