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We study linear stability of solutions to the Navier\textendash Stokesequations with stochastic viscosity. Specifically, we assume that the viscosityis given in the form of a~stochastic expansion. Stability analysis requires asolution of the steady-state Navier-Stokes equation and then leads to ageneralized eigenvalue problem, from which we wish to characterize the realpart of the rightmost eigenvalue. While this can be achieved by Monte Carlosimulation, due to its computational cost we study three surrogates based ongeneralized polynomial chaos, Gaussian process regression and a shallow neuralnetwork. The results of linear stability analysis assessment obtained by thesurrogates are compared to that of Monte Carlo simulation using a set ofnumerical experiments.

On Surrogate Learning for Linear Stability Assessment of Navier-Stokes Equations with Stochastic Viscosity