From the 1 of 6 linked papers with an AI index.
7 papers
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
The paper applies quasi‑Monte Carlo methods to efficiently propagate uncertainty through a semi‑linear parabolic reaction‑diffusion model of tumor growth, demonstrating faster conv…
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…
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…
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 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…
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…