标题： 一种分析和人工智能发现的稳定、准确且可推广的地理物理湍流亚网格闭合方法 显示英文标题

标题： An Analytical and AI-discovered Stable, Accurate, and Generalizable Subgrid-scale Closure for Geophysical Turbulence

摘要： 通过结合人工智能和流体物理，我们从少量直接数值模拟（DNS）数据中发现了一个二维湍流的显式闭合表达式。 使用该闭合方法的大涡模拟（LES）准确且稳定，能够再现DNS统计结果，包括极端情况的统计结果。 我们还表明，新的闭合表达式可以从四阶截断的泰勒展开中推导出来。 先前的分析方法和基于人工智能的工作仅找到了二阶展开，这导致了不稳定的LES。 只有在稀疏方程发现中同时考虑尺度间能量传递和标准重构准则时，这些额外项才会出现。 显示英文摘要

摘要： 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.