Geodesic
On surrogate learning for linear stability assessment of Navier-Stokes equations with stochastic viscosity
Applications of Mathematics, Tome 67 (2022) no. 6, pp. 727-749.

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We study linear stability of solutions to the Navier-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.
DOI : 10.21136/AM.2022.0046-21
Classification : 35R60, 60H35, 65C30
Keywords: linear stability; Navier-Stokes equations; generalized polynomial chaos; stochastic collocation; stochastic Galerkin method; Gaussian process regression; shallow neural network 
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Sousedík, Bedřich; Elman, Howard C.; Lee, Kookjin; Price, Randy. On surrogate learning for linear stability assessment of Navier-Stokes equations with stochastic viscosity. Applications of Mathematics, Tome 67 (2022) no. 6, pp. 727-749. doi : 10.21136/AM.2022.0046-21. http://geodesic.mathdoc.fr/articles/10.21136/AM.2022.0046-21/

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