We introduce a simple, stochastic, a-posteriori, turbulence closure model based on a reduced subgrid scale term. This subgrid scale term is tailor-made to capture the statistics of a small set of spatially-integrate quantities of interest (QoIs), with only one unresolved scalar time series per QoI. In contrast to other data-driven surrogates the dimension of the "learning problem" is reduced from an evolving field to one scalar time series per QoI. We use an a-posteriori, nudging approach to find the distribution of the scalar series over time. This approach has the advantage of taking the interaction between the solver and the surrogate into account. A stochastic surrogate parametrization is obtained by random sampling from the found distribution for the scalar time series. Compared to an a-priori trained convolutional neural network, evaluating the new method is computationally much cheaper and gives similar long-term statistics.

翻译：本文提出一种基于简化子网格项的简单随机后验湍流闭合模型。该子网格项专为捕捉少量空间积分关注量（QoIs）的统计特性而设计，每个QoI仅需一个未解析标量时间序列。与其他数据驱动代理模型相比，"学习问题"的维度从演化场简化为每个QoI对应的单个标量时间序列。我们采用后验引导方法来确定标量序列随时间变化的分布规律，该方法具有考虑求解器与代理模型交互作用的优势。通过对标量时间序列的分布进行随机采样，获得随机代理参数化方案。与先验训练的卷积神经网络相比，新方法的计算成本显著降低，且能获得相似的长期统计特性。