60 citations · 61 across the 7 of their papers we have counts for
10 papers
A higher order lattice-based method for high-dimensional numerical integration using periodization
Felix Bartel, Alexander D. Gilbert, Michael Griebel +2
We present a novel numerical integration method for non-periodic functions over the high-dimensional unit cube by a specially crafted (unequally-)weighted quadrature rule…
Vector-Valued Gaussian Processes for Approximating Divergence- or Rotation-free Vector Fields
Quoc Thong Le Gia, Ian Hugh Sloan, Holger Wendland
In this paper, we discuss vector-valued Gaussian processes for the approximation of divergence- or rotation-free functions. We establish the theory for such Gaussian processes, the…
Quasi-Monte Carlo methods for uncertainty quantification of tumor growth modeled by a parametric semi-linear parabolic reaction-diffusion equation
Alexander D. Gilbert, Frances Y. Kuo, Dirk Nuyens +3
We study the application of a quasi-Monte Carlo (QMC) method to a class of semi-linear parabolic reaction-diffusion partial differential equations used to model tumor growth. Mathe…
Minimal Subsampled Rank-1 Lattices for Multivariate Approximation with Optimal Convergence Rate
Felix Bartel, Alexander D. Gilbert, Frances Y. Kuo +1
In this paper we show error bounds for randomly subsampled rank-1 lattices. We pay particular attention to the ratio of the size of the subset to the size of the initial lattice, w…
Multilevel lattice-based kernel approximation for elliptic PDEs with random coefficients
Alexander D. Gilbert, Michael B. Giles, Frances Y. Kuo +2
This paper introduces a multilevel kernel-based approximation method to estimate efficiently solutions to elliptic partial differential equations (PDEs) with periodic random coeffi…
Regularity and tailored regularization of Deep Neural Networks, with application to parametric PDEs in uncertainty quantification
Alexander Keller, Frances Y. Kuo, Dirk Nuyens +1
In this paper we consider Deep Neural Networks (DNNs) with a smooth activation function as surrogates for high-dimensional functions that are somewhat smooth but costly to evaluate…
Quasi-Monte Carlo methods for uncertainty quantification of wave propagation and scattering problems modelled by the Helmholtz equation
Ivan G. Graham, Frances Y. Kuo, Dirk Nuyens +2
We analyse and implement a quasi-Monte Carlo (QMC) finite element method (FEM) for the forward problem of uncertainty quantification (UQ) for the Helmholtz equation with random coe…
Removing the mask -- reconstructing a scalar field on the sphere from a masked field
Jan Hamann, Quoc Thong Le Gia, Ian H. Sloan +1
The paper analyses a spectral approach to reconstructing a scalar field on the sphere, given only information about a masked version of the field together with precise information…
On approximation for time-fractional stochastic diffusion equations on the unit sphere
T. Alodat, Q. T. Le Gia, I. H. Sloan
This paper develops a two-stage stochastic model to investigate evolution of random fields on the unit sphere $\bS^2$ in . The model is defined by a time-fractional stochasti…
On Wavelet-Galerkin methods for Semilinear Parabolic Equations with Additive Noise
M. Kovács, S. Larsson, K. Urban
We consider the semilinear stochastic heat equation perturbed by additive noise. After time-discretization by Euler's method the equation is split into a linear stochastic equation…