4 papers
Fourier Neural Operators with rank-1 lattice points and hyperbolic cross
Jakob Dilen, Alexander Keller, Frances Y. Kuo +1
The \emph{Fourier neural operator} (FNO) is a neural network architecture that learns mappings between function spaces. Its efficient implementation is based on the multi-dimension…
Lattice-based Deep Neural Networks: Regularity and Tailored Regularization
Alexander Keller, Frances Y. Kuo, Dirk Nuyens +1
This survey article is concerned with the application of lattice rules to Deep Neural Networks (DNNs), lattice rules being a family of quasi-Monte Carlo methods. They have demonstr…
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…