Stochastic Reconstruction of Gappy Lagrangian Turbulent Signals by Conditional Diffusion Models

TL;DR

This paper introduces a novel stochastic reconstruction method using conditional diffusion models to recover missing Lagrangian turbulent signals, effectively capturing complex scale-dependent properties and correlations in diverse turbulent flow scenarios.

Contribution

The paper presents the first application of conditional diffusion models for reconstructing Lagrangian turbulent signals with high accuracy and flexibility, outperforming Gaussian process regressions.

Findings

Successfully reconstructs 3D turbulent velocity signals with non-Gaussian features.

Accurately recovers 2D trajectories from ocean drifters, preserving statistical properties.

Demonstrates superior performance over traditional Gaussian methods.

Abstract

We present a stochastic method for reconstructing missing spatial and velocity data along the trajectories of small objects passively advected by turbulent flows with a wide range of temporal or spatial scales, such as small balloons in the atmosphere or drifters in the ocean. Our approach makes use of conditional generative diffusion models, a recently proposed data-driven machine learning technique. We solve the problem for two paradigmatic open problems, the case of 3D tracers in homogeneous and isotropic turbulence, and 2D trajectories from the NOAA-funded Global Drifter Program. We show that for both cases, our method is able to reconstruct velocity signals retaining non-trivial scale-by-scale properties that are highly non-Gaussian and intermittent. A key feature of our method is its flexibility in dealing with the location and shape of data gaps, as well as its ability to naturally exploit correlations between different components, leading to superior accuracy, with respect to Gaussian process regressions, for both pointwise reconstruction and statistical expressivity. Our method shows promising applications also to a wide range of other Lagrangian problems, including multi-particle dispersion in turbulence, dynamics of charged particles in astrophysics and plasma physics, and pedestrian dynamics.