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

被引：1

作者：

Sousedik, Bedrich ^{[1
]}

Elman, Howard C. ^{[2
,3
]}

Lee, Kookjin ^{[4
]}

Price, Randy ^{[5
,6
]}

机构：

[1] Univ Maryland Baltimore Cty, Dept Math & Stat, 1000 Hilltop Circle, Baltimore, MD 21250 USA

[2] Univ Maryland, Dept Comp Sci, College Pk, MD 20742 USA

[3] Univ Maryland, Inst Adv Comp Studies, Iribe Ctr, 8125 Paint Branch Dr, College Pk, MD 20742 USA

[4] Arizona State Univ, Sch Comp & Augmented Intelligence, 699 S Mill Ave, Tempe, AZ 85281 USA

[5] George Mason Univ, Ctr Math & Artificial Intelligence, 4400 Univ Dr,MS 3F2,Exploratory Hall,Room 4102, Fairfax, VA 22030 USA

[6] George Mason Univ, Ctr Computat Fluid Dynam, 4400 Univ Dr,MS 3F2,Exploratory Hall,Room 4102, Fairfax, VA 22030 USA

来源：

APPLICATIONS OF MATHEMATICS | 2022年 / 67卷 / 06期

基金：

美国国家科学基金会;

关键词：

linear stability; Navier-Stokes equations; generalized polynomial chaos; stochastic collocation; stochastic Galerkin method; Gaussian process regression; shallow neural network; GALERKIN METHODS; INTEGRATION;

D O I：

10.21136/AM.2022.0046-21

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：727 / 749

页数：23

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