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：本文提出并分析了用于随机斯托克斯和纳维-斯托克斯问题的加权降阶方法，这些问题的解依赖于随机输入数据（如力项、物理或几何系数、边界条件）。我们将比较加权方法（如加权贪婪法和加权POD）与非加权方法在随机参数情形下的性能。此外，我们将分析不同的采样和加权策略，以克服高维参数空间带来的维度灾难。