In this manuscript we propose and analyze weighted reduced order methods for stochastic Stokes and Navier-Stokes problems depending on random input data (such as forcing terms, physical or geometrical coefficients, boundary conditions). We will compare weighted methods such as weighted greedy and weighted POD with non-weighted ones in case of stochastic parameters. In addition we will analyze different sampling and weighting choices to overcome the curse of dimensionality with high dimensional parameter spaces.

翻译：本文中，我们提出并分析加权降阶方法用于依赖于随机输入数据的随机 Stokes 方程和 Navier-Stokes 问题（如强制项、物理或几何系数、边界条件等）。我们将比较加权贪心法和加权 POD 与非加权方法在随机参数的情况下的效果。此外，我们还将分析不同的采样和加权选择，以解决高维参数空间中的维数灾难问题。