An Analytical and AI-discovered Stable, Accurate, and Generalizable Subgrid-scale Closure for Geophysical Turbulence
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Abstract (arXiv)
By combining AI and fluid physics, we discover a closed-form closure for 2D turbulence from small direct numerical simulation (DNS) data. Large-eddy simulation (LES) with this closure is accurate and stable, reproducing DNS statistics including those of extremes. We also show that the new closure could be derived from a 4th-order truncated Taylor expansion. Prior analytical and AI-based work only found the 2nd-order expansion, which led to unstable LES. The additional terms emerge only when inter-scale energy transfer is considered alongside standard reconstruction criterion in the sparse-equation discovery.
Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 10 of its 92 references that are in the map. First posted on arXiv 5 Sep 2025.
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10 of 92 references.
References · 10
- 2019AI Feynman: a Physics-Inspired Method for Symbolic Regressioncited by 548
- 2019Machine Learning for Fluid Mechanicscited by 385
- 2021Scientific multi-agent reinforcement learning for wall-models of turbulent flowscited by 52
- 2021Any equation is a forest: Symbolic genetic algorithm for discovering open-form partial differential equations (SGA-PDE)cited by 41
- 2022Explaining the physics of transfer learning a data-driven subgrid-scale closure to a different turbulent flowcited by 20
- 2022Deep Reinforcement Learning for Turbulence Modeling in Large Eddy Simulationscited by 16
- 2023Learning Closed-form Equations for Subgrid-scale Closures from High-fidelity Data: Promises and Challengescited by 9
- 2021Discovery of interpretable structural model errors by combining Bayesian sparse regression and data assimilation: A chaotic Kuramoto-Sivashinsky test casecited by 6
- 2024Coarse Graining with Neural Operators for Simulating Chaotic Systemscited by 6
- 2025Stochastic and Non-local Closure Modeling for Nonlinear Dynamical Systems via Latent Score-based Generative Modelscited by 4
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Citing papers per year: 2026: 1.
1 paper.