  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.
