In this paper we propose a Bayesian method as a numerical way to correct and stabilise projection-based reduced order models (ROM) in computational fluid dynamics problems. The approach is of hybrid type, and consists of the classical proper orthogonal decomposition driven Galerkin projection of the laminar part of the governing equations, and Bayesian identification of the correction term mimicking both the turbulence model and possible ROM-related instabilities given the full order data. In this manner the classical ROM approach is translated to the parameter identification problem on a set of nonlinear ordinary differential equations. Computationally the inverse problem is solved with the help of the Gauss-Markov-Kalman smoother in both ensemble and square-root polynomial chaos expansion forms. To reduce the dimension of the posterior space, a novel global variance based sensitivity analysis is proposed.

中文翻译：

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用于计算流体动力学的基于投影的降阶模型的贝叶斯识别

在本文中，我们提出了一种贝叶斯方法，作为在计算流体动力学问题中校正和稳定基于投影的降阶模型 (ROM) 的数值方法。该方法是混合型的，包括控制方程层流部分的经典适当正交分解驱动的伽辽金投影，以及在给定全阶数据的情况下模拟湍流模型和可能的 ROM 相关不稳定性的校正项的贝叶斯识别. 以这种方式，经典的 ROM 方法被转化为一组非线性常微分方程的参数识别问题。在计算上，借助高斯-马尔可夫-卡尔曼平滑器以集成和平方根多项式混沌展开形式解决逆问题。为了减少后验空间的维数，