Stochastic Generation of Lagrangian Turbulent Signals by Conditional Generative Diffusion Models*

Lagrangian turbulence lies at the core of numerous applied and fundamental problems related to the physics of dispersion and mixing in engineering, biofluids, the atmosphere, oceans, and astrophysics. Despite exceptional theoretical, numerical, and experimental efforts conducted over the past 30 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 full 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 reproduce most statistical benchmarks across time scales, including the fat-tail distribution for velocity increments, the anomalous power law and the increased intermittency around the dissipative scale. We also discuss the applicability of the same method to reconstruct partially sampled trajectories, highlighting the adaptability of this approach to different scenarios; we discuss applications to both the reconstruction of tracer particles from three-dimensional DNS of turbulent flows, as well as the reconstruction of trajectories of oceanic drifters released by the Global Drifter Program (GDP).