
A numerical approach to Kolmogorov equation in high dimension based on Gaussian analysis
For Kolmogorov equations associated to finite dimensional stochastic dif...
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Uncertainty Quantification in Stochastic Economic Dispatch using Gaussian Process Emulation
The increasing penetration of renewable energy resources in power system...
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Intrusive and NonIntrusive Polynomial Chaos Approximations for a TwoDimensional Steady State NavierStokes System with Random Forcing
While convergence of polynomial chaos approximation for linear equations...
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Probabilistic forecast of multiphase transport under viscous and buoyancy forces in heterogeneous porous media
In this study, we develop a probabilistic approach to map the parametric...
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Particle Filtering for Stochastic NavierStokes Signal Observed with Linear Additive Noise
We consider a nonlinear filtering problem, whereby the signal obeys the...
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Multilevel quasiMonte Carlo for random elliptic eigenvalue problems I: Regularity and error analysis
Random eigenvalue problems are useful models for quantifying the uncerta...
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Hysteresis and Linear Stability Analysis on Multiple SteadyState Solutions to the Poisson–Nernst–Planck equations with Steric Interactions
In this work, we numerically study linear stability of multiple steadys...
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On Surrogate Learning for Linear Stability Assessment of NavierStokes Equations with Stochastic Viscosity
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 steadystate NavierStokes 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.
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