Analytical and AI-Discovered Stable, Accurate, and Generalizable Subgrid-Scale Closure for Geophysical Turbulence
Published in Physical Review Letters, 2026
Recommended citation: Karan Jakhar, Yifei Guan, and Pedram Hassanzadeh. "Analytical and AI-Discovered Stable, Accurate, and Generalizable Subgrid-Scale Closure for Geophysical Turbulence." Physical Review Letters 136, no. 6 (2026): 064201. https://doi.org/10.1103/v28b-5qmp
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.
Recommended citation: Karan Jakhar, Yifei Guan, and Pedram Hassanzadeh. “Analytical and AI-Discovered Stable, Accurate, and Generalizable Subgrid-Scale Closure for Geophysical Turbulence.” Physical Review Letters 136, no. 6 (2026): 064201.