Synthetic Lagrangian Turbulence by Generative Diffusion Models
Tianyi Li Luca Biferale Fabio Bonaccorso Martino Andrea Scarpolini Michele Buzzicotti
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.