AI结合流体物理发现稳定精准的湍流亚格子闭合方案
An Analytical and AI-discovered Stable, Accurate, and Generalizable Subgrid-scale Closure for Geophysical Turbulence
- 基于小规模直接数值模拟数据，用AI与物理约束联合发现闭合公式
- 大涡模拟使用该方案后稳定且准确，能复现极端统计特征
- 首次通过高阶展开推导出稳定解，适合气候与海洋建模研究者
通过结合人工智能与流体物理，我们仅用少量直接数值模拟（DNS）数据，从2维湍流中发现了一个闭式亚格子尺度闭合。采用该闭合的大涡模拟（LES）在精度和稳定性上表现优异，能够重现包括极端情况在内的完整DNS统计特性。我们还证明该闭合可由四阶截断泰勒展开推导得出。以往的解析与基于AI的工作仅发现二阶展开，导致LES不稳定。新增项仅在同时考虑跨尺度能量传递与稀疏方程发现中的标准重构准则时出现。
原文摘要 · Abstract (English)
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.
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