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.

翻译：通过结合人工智能与流体物理学，我们从小型直接数值模拟（DNS）数据中发现了一种用于二维湍流的闭合形式闭合模型。采用该闭合模型的大涡模拟（LES）具有高精度与稳定性，能够复现包括极端统计量在内的DNS统计特性。我们还证明，这一新闭合模型可通过四阶截断泰勒展开推导得出。先前基于解析与人工智能的研究仅发现了二阶展开，这导致了不稳定的LES。只有当在稀疏方程发现中同时考虑跨尺度能量传递与标准重构准则时，这些附加项才会显现。