33 citations · 48 across the 19 of their papers we have counts for
11 papers · 1 filter
Optimal numerical integration for functions in fractional Gaussian Sobolev spaces
Van Kien Nguyen
This paper investigates the numerical approximation of integrals for functions in fractional Gaussian Sobolev spaces with dominating mixed smoothness defi…
Approximation of PDE solution manifolds: Sparse-grid interpolation and quadrature
Dinh Dũng, Van Kien Nguyen, Duong Thanh Pham +1
We study fully-discrete approximations and quadratures of infinite-variate functions in abstract Bochner spaces associated with a Hilbert space and an infinite-tensor-product J…
Optimal numerical integration and approximation of functions on equipped with Gaussian measure
Dinh Dũng, Van Kien Nguyen
We investigate the numerical approximation of integrals over equipped with the standard Gaussian measure for integrands belonging to the Gaussian-weighted Sobole…
Analyticity of Parametric Elliptic Eigenvalue Problems and Applications to Quasi-Monte Carlo Methods
Van Kien Nguyen
In the present paper, we study the analyticity of the leftmost eigenvalue of the linear elliptic partial differential operator with random coefficient and analyze the convergence r…
Analyticity and sparsity in uncertainty quantification for PDEs with Gaussian random field inputs
Dinh Dũng, Van Kien Nguyen, Christoph Schwab +1
We establish sparsity and summability results for coefficient sequences of Wiener-Hermite polynomial chaos expansions of countably-parametric solutions of linear elliptic and parab…
Deep ReLU neural network approximation in Bochner spaces and applications to parametric PDEs
Dinh Dũng, Van Kien Nguyen, Duong Thanh Pham
We investigate non-adaptive methods of deep ReLU neural network approximation in Bochner spaces of functions on taking values i…
High-dimensional nonlinear approximation by parametric manifolds in Hölder-Nikol'skii spaces of mixed smoothness
Dinh Dũng, Van Kien Nguyen
We study high-dimensional nonlinear approximation of functions in Hölder-Nikol'skii spaces on the unit cube having mixed smoothne…
Deep ReLU neural networks in high-dimensional approximation
Dinh Dũng, Van Kien Nguyen
We study the computation complexity of deep ReLU (Rectified Linear Unit) neural networks for the approximation of functions from the Hölder-Zygmund space of mixed smoothness define…
Unified Analysis of Periodization-Based Sampling Methods for Matérn Covariances
Markus Bachmayr, Ivan G. Graham, Van Kien Nguyen +1
The periodization of a stationary Gaussian random field on a sufficiently large torus comprising the spatial domain of interest is the basis of various efficient computational meth…
Monte Carlo Methods for Uniform Approximation on Periodic Sobolev Spaces with Mixed Smoothness
Glenn Byrenheid, Robert J. Kunsch, Van Kien Nguyen
We consider the order of convergence for linear and nonlinear Monte Carlo approximation of compact embeddings from Sobolev spaces of dominating mixed smoothness defined on the toru…
Change of variable in spaces of mixed smoothness and numerical integration of multivariate functions on the unit cube
Van Kien Nguyen, Mario Ullrich, Tino Ullrich
In a recent article by two of the present authors it turned out that Frolov's cubature formulae are optimal and universal for various settings (Besov-Triebel-Lizorkin spaces) of fu…