We study linear stability of solutions to the Navier\textendash Stokes equations with stochastic viscosity. Specifically, we assume that the viscosity is given in the form of a~stochastic expansion. Stability analysis requires a solution of the steady-state Navier-Stokes equation and then leads to a generalized eigenvalue problem, from which we wish to characterize the real part of the rightmost eigenvalue. While this can be achieved by Monte Carlo simulation, due to its computational cost we study three surrogates based on generalized polynomial chaos, Gaussian process regression and a shallow neural network. The results of linear stability analysis assessment obtained by the surrogates are compared to that of Monte Carlo simulation using a set of numerical experiments.

翻译：我们研究Navier\ textendash Stokes等方程式的线性稳定性。 具体地说, 我们假设, 粘度是以 ~ 随机扩张的形式给出的。 稳定分析需要稳定状态 Navier- Stokes 等方程式的解决方案, 然后导致一个普遍的电子价值问题, 我们希望从中找到最右半基因价值的真正部分。 虽然这可以通过蒙特卡洛模拟实现, 因为它的计算成本, 我们根据普遍的多边混乱、 高山进程回归和浅线性网络来研究三个代孕。 代孕者获得的线性稳定性分析评估的结果与使用一组数字实验来比较蒙特卡洛模拟的结果。