On surrogate learning for linear stability assessment of Navier-Stokes equations with stochastic viscosity

Bedřich Sousedík; Howard C. Elman; Kookjin Lee; Randy Price

Applications of Mathematics (2022)

  • Volume: 67, Issue: 6, page 727-749
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Sousedík, Bedřich, et al. "On surrogate learning for linear stability assessment of Navier-Stokes equations with stochastic viscosity." Applications of Mathematics 67.6 (2022): 727-749. <http://eudml.org/doc/298506>.

@article{Sousedík2022,
abstract = {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.},
author = {Sousedík, Bedřich, Elman, Howard C., Lee, Kookjin, Price, Randy},
journal = {Applications of Mathematics},
keywords = {linear stability; Navier-Stokes equations; generalized polynomial chaos; stochastic collocation; stochastic Galerkin method; Gaussian process regression; shallow neural network},
language = {eng},
number = {6},
pages = {727-749},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On surrogate learning for linear stability assessment of Navier-Stokes equations with stochastic viscosity},
url = {http://eudml.org/doc/298506},
volume = {67},
year = {2022},
}

TY - JOUR
AU - Sousedík, Bedřich
AU - Elman, Howard C.
AU - Lee, Kookjin
AU - Price, Randy
TI - On surrogate learning for linear stability assessment of Navier-Stokes equations with stochastic viscosity
JO - Applications of Mathematics
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 67
IS - 6
SP - 727
EP - 749
AB - 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.
LA - eng
KW - linear stability; Navier-Stokes equations; generalized polynomial chaos; stochastic collocation; stochastic Galerkin method; Gaussian process regression; shallow neural network
UR - http://eudml.org/doc/298506
ER -

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