On uncertainty quantification in hydrogeology and hydrogeophysics
Recent advances in sensor technologies, field methodologies, numerical modeling, and
inversion approaches have contributed to unprecedented imaging of hydrogeological …
inversion approaches have contributed to unprecedented imaging of hydrogeological …
Multi-index stochastic collocation for random PDEs
In this work we introduce the Multi-Index Stochastic Collocation method (MISC) for
computing statistics of the solution of a PDE with random data. MISC is a combination …
computing statistics of the solution of a PDE with random data. MISC is a combination …
Convergence of quasi-optimal sparse-grid approximation of Hilbert-space-valued functions: application to random elliptic PDEs
In this work we provide a convergence analysis for the quasi-optimal version of the sparse-
grids stochastic collocation method we presented in a previous work:“On the optimal …
grids stochastic collocation method we presented in a previous work:“On the optimal …
Convergence of sparse collocation for functions of countably many Gaussian random variables (with application to elliptic PDEs)
We give a convergence proof for the approximation by sparse collocation of Hilbert-space-
valued functions depending on countably many Gaussian random variables. Such functions …
valued functions depending on countably many Gaussian random variables. Such functions …
An adaptive sparse grid algorithm for elliptic PDEs with lognormal diffusion coefficient
In this work we build on the classical adaptive sparse grid algorithm (T. Gerstner and M.
Griebel, Dimension-adaptive tensor-product quadrature), obtaining an enhanced version …
Griebel, Dimension-adaptive tensor-product quadrature), obtaining an enhanced version …
[PDF][PDF] 不确定性量化的高精度数值方法和理论
汤涛， 周涛 - 中国科学: 数学, 2015 - math.hkbu.edu.hk
摘要不确定性量化(Uncertainty Quantification, UQ) 是近年来国际上热门的研究课题,
其应用领域包括水文学, 流体力学, 数据同化, 天气预测等等. 由于UQ 问题中的大量随机参数 …
其应用领域包括水文学, 流体力学, 数据同化, 天气预测等等. 由于UQ 问题中的大量随机参数 …
A Multi Level Monte Carlo method with control variate for elliptic PDEs with log-normal coefficients
F Nobile, F Tesei - Stochastic Partial Differential Equations: Analysis and …, 2015 - Springer
We consider the numerical approximation of the stochastic Darcy problem with log-normal
permeability field and propose a novel Multi Level Monte Carlo (MLMC) approach with a …
permeability field and propose a novel Multi Level Monte Carlo (MLMC) approach with a …
Sparse quadrature for high-dimensional integration with Gaussian measure
P Chen - ESAIM: Mathematical Modelling and Numerical …, 2018 - numdam.org
In this work we analyze the dimension-independent convergence property of an abstract
sparse quadrature scheme for numerical integration of functions of high-dimensional …
sparse quadrature scheme for numerical integration of functions of high-dimensional …
On discrete least-squares projection in unbounded domain with random evaluations and its application to parametric uncertainty quantification
This work is concerned with approximating multivariate functions in an unbounded domain
by using a discrete least-squares projection with random point evaluations. Particular …
by using a discrete least-squares projection with random point evaluations. Particular …
IGA-based multi-index stochastic collocation for random PDEs on arbitrary domains
This paper proposes an extension of the Multi-Index Stochastic Collocation (MISC) method
for forward uncertainty quantification (UQ) problems in computational domains of shape …
for forward uncertainty quantification (UQ) problems in computational domains of shape …