Multi-Scale Reconstruction of Turbulent Rotating Flows with Generative Diffusion Models

• Published in: Atmosphere Vol. 15; no. 1; p. 60
• Main Authors: Li, Tianyi, Lanotte, Alessandra S., Buzzicotti, Michele, Bonaccorso, Fabio, Biferale, Luca
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.01.2024
• Subjects: Data augmentation; Diffusion; Diffusion models; Electronic data processing; flow reconstruction; Fluid dynamics; Fluid mechanics; Generative adversarial networks; Geophysics; Machine learning; Missing data; Neural networks; Probability distribution; Reconstruction; Reynolds number; Risk assessment; rotating turbulence; Rotation; Statistical analysis; Statistics; Three dimensional flow; Turbulence; Turbulent diffusion; Velocity distribution; Italy
• ISSN: 2073-4433; 2073-4433
• DOI: 10.3390/atmos15010060

We address the problem of data augmentation in a rotating turbulence set-up, a paradigmatic challenge in geophysical applications. The goal is to reconstruct information in two-dimensional (2D) cuts of the three-dimensional flow fields, imagining spatial gaps present within each 2D observed slice. We evaluate the effectiveness of different data-driven tools, based on diffusion models (DMs), a state-of-the-art generative machine learning protocol, and generative adversarial networks (GANs), previously considered as the best-performing method both in terms of point-wise reconstruction and the statistical properties of the inferred velocity fields. We focus on two different DMs recently proposed in the specialized literature: (i) RePaint, based on a heuristic strategy to guide an unconditional DM for flow generation by using partial measurements data, and (ii) Palette, a conditional DM trained for the reconstruction task with paired measured and missing data. Systematic comparison shows that (i) DMs outperform the GAN in terms of the mean squared error and/or the statistical accuracy; (ii) Palette DM emerges as the most promising tool in terms of both point-wise and statistical metrics. An important property of DMs is their capacity for probabilistic reconstructions, providing a range of predictions based on the same measurements, enabling uncertainty quantification and risk assessment.