Projects
Applications and Analysis of Lattice Points: Time-stepping and Integration over Rd KU Leuven
We study numerical methods for function approximation and numerical integration. Specifically, we study so called "quasi-Monte Carlo" (QMC) methods. QMC methods are widely used thechniques using deterministic point sets whereas Monte Carlo methods use (pseudo-) random numbers. QMC methods in high dimensions can usually be more efficient than other methods when the problem has a specific high-dimensional structure. Since high-dimensional ...
From full-field data to spatial uncertainty KU Leuven
“Lighter is better” is quickly becoming a new mantra in mechanical engineering designs, leading to structures that are becoming increasingly designed up to their performance limits. As a result, uncertainty quantification (UQ) is quickly gaining in importance to assess the reliability of these structures, given typical variability and/or uncertainty an analyst is faced with. However, these reliability estimates are only as accurate as the ...
Cubature for infinite-dimensional problems KU Leuven
The aim of this project is to study cubature methods for infinite-dimensional integrals. We will consider multilevel algorithms as well as more general dimension decomposition methods in combination with Monte Carlo, quasi-Monte Carlo [2,8], sparse grids [3] and classical cubature methods.
Sabbatical Dirk Nuyens: Discovering future goals of lattice based cubature. KU Leuven
The aim of the sabbatical is to make large progress on a joint project and to start defining future goals based on early results from the scope of the project. The project is developing new theory and analyzes new algorithms for calculating expected values, and otheer miments of quantities of interest, obtained form complicated mathematical models.
Variations on Component-by-Component Construction Algorithms of Lattice Rules KU Leuven
In the conducted research we develop efficient algorithms for constructing node sets of high-quality quasi-Monte Carlo (QMC) methods which can be used for approximating high-dimensional integrals of multivariate functions. In particular, we study the construction of rank-1 lattice rules and polynomial lattice rules, which are both specified by a generating vector, for numerical integration in weighted function spaces such as Korobov, Sobolev ...
Quantum kinetics of exciton polaritons University of Antwerp
Neutrino-nucleus interactions : towards a microscopic description of exclusive quasi-elastic processes Ghent University
One of the remaining big mysteries in physics is the matter dominance of the universe. We have no idea why our universe consists of matter, while almost no antimatter survived the fiery aftermath of the Big Bang. Worldwide, neutrino oscillation experiments are preparing for a decisive quest in this investigation. In these experiments, this asymmetry would show up as a small difference between the oscillation probability for neutrinos and for ...