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Analytical and AI-Discovered Stable, Accurate, and Generalizable Subgrid-Scale Closure for Geophysical Turbulence

Karan Jakhar1,2, Yifei Guan1,3, and Pedram Hassanzadeh4,*

  • 1Department of Geophysical Sciences, University of Chicago, Chicago, Illinois 60637, USA
  • 2Department of Mechanical Engineering, Rice University, Houston, Texas 77005, USA
  • 3Department of Mechanical Engineering, Union College, Schenectady, New York 12308, USA
  • 4Department of Geophysical Sciences and Committee on Computational and Applied Mathematics, University of Chicago, Chicago, Illinois 60637, USA

  • *Contact author: pedramh@uchicago.edu
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Phys. Rev. Lett. 136, 064201 – Published 10 February, 2026

DOI: https://doi.org/10.1103/v28b-5qmp

Abstract

By combining artificial intelligence and fluid physics, we discover a closed-form closure for 2D turbulence from small direct numerical simulation data. Large-eddy simulation with this closure is accurate and stable, reproducing direct numerical simulation statistics, including those of extremes. We also show that the new closure could be derived from a fourth-order truncated Taylor expansion. Prior analytical and artificial-intelligence-based work only found the second-order expansion, which led to unstable large-eddy simulation. The additional terms emerge only when interscale energy transfer is considered alongside standard reconstruction criterion in the sparse-equation discovery.

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synopsis

AI Discovers Geophysical Turbulence Model

Published 10 February, 2026

Researchers have used an artificial-intelligence tool to reveal long-sought equations that describe small-scale features in 2D turbulent systems.

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Phys. Rev. Lett. 136, 064201– Published 10 February, 2026
  • Received 5 September 2025
  • Accepted 22 December 2025
Article part of CHORUS
Accepted manuscript will be available starting 10 February, 2027.
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