关于具有随机粘度的纳维-斯托克斯方程线性稳定性评估的代理学习
On Surrogate Learning for Linear Stability Assessment of Navier-Stokes Equations with Stochastic Viscosity
AI总结：
本文提出三种代理方法用于评估具有随机粘度的纳维-斯托克斯方程的线性稳定性，并通过实验验证其有效性。
摘要：
我们研究了具有随机粘度的纳维-斯托克斯方程解的线性稳定性。具体来说，我们假设粘度以随机展开形式给出。稳定性分析需要求解稳态纳维-斯托克斯方程，进而导致一个广义特征值问题，我们希望表征右端特征值的实部。虽然这可以通过蒙特卡罗模拟实现，但由于其计算成本，我们研究了三种基于广义多项式 chaos、高斯过程回归和浅层神经网络的代理方法。通过一组数值实验，将代理方法获得的线性稳定性分析结果与蒙特卡罗模拟结果进行比较。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
