Synthetic Lagrangian Turbulence by Generative Diffusion Models
This provides a method to generate synthetic Lagrangian turbulence data for applications in engineering, bio-fluids, and environmental sciences, though it is incremental as it adapts an existing diffusion model to a specific domain.
The authors tackled the problem of generating realistic single-particle trajectories in three-dimensional turbulence at high Reynolds numbers, using a diffusion model to reproduce key statistical benchmarks like fat-tail velocity distributions and anomalous power laws, with slight deviations at small scales but strong generalizability for extreme events.
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 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. Slight deviations are observed below the dissipative scale, particularly in the acceleration and flatness statistics. Surprisingly, the model exhibits strong generalizability for extreme events, producing events of higher intensity and rarity that still match the realistic statistics. This paves the way for producing synthetic high-quality datasets for pre-training various downstream applications of Lagrangian turbulence.