PhD Position in Chebyshev Lattice Algorithms for High-Dimensional Integration

Catholic University of Leuven Department of Computer Science


NUMA is a research section within the Department of Computer Science of KU Leuven, with 12 permanent staff members and approximately 40 PhD and postdoctoral researchers. NUMA works on the crossing of numerical analysis and computational mathematics and develops numerical algorithms and software for large-scale problems in science and engineering. This position is on a project in cooperation with the research group of Frances Kuo of the School of Mathematics and Statistics of the University of New South Wales, Sydney, Australia.


This position is part of an FWO project in cooperation with UNSW Sydney which develops new algorithms for approximating high dimensional integrals.

Very high dimensional integrals are one of the most challenging problems in computational mathematics and in particular in the theoretical development of Uncertainty Quantification techniques (a very hot topic these days).

To approximate high dimensional integrals we make use of sampling point sets based on lattices. The simplest form are "lattice rules" and they have been extensively studied, mostly in the worst case setting, by the project supervisors (both in Leuven and in Sydney).
This project extends the analysis of lattice based methods to higher order convergence in non-periodic spaces aiming for optimal randomized error bounds.
Very recently the supervisors were able to formulate a complete framework for approximating non-periodic functions in a multivariate Chebyshev basis using FFT-based algorithms on lattice based sampling points.
However, a lot of the theory which we normally have available to analyse numerical integration is still missing.
There are two PhD positions on this project. This job posting is concerned with pushing the limits for Chebyshev lattice methods and will develop both the worst case error analysis as well as root mean squared error analysis for a recently discovered randomized algorithm.
The two PhD students will also work together on a more general framework for the randomization of lattice based point sets.


  • Hold a Master in Mathematical Engineering, Mathematics, Computational Mathematics or equivalent
  • Solid background and interest in numerical analysis and computational mathematics
  • Experience with programming and developing scientific software
  • Persistent and proud of your work
  • Excellent proficiency in English and good oral and written communication skills


  • A high-level and exciting international research environment
  • The opportunity to build research and innovation skills that are essential for a future career in research and development
  • Funding is secured for four years, the initial offer is a one-year appointment, renewal depends on the progress in the PhD program
  • A competitive salary


For more information please contact Prof. dr. ir. Dirk Nuyens, tel.: +32 16 37 35 59, mail: or Prof. dr. ir. Ronald Cools, tel.: +32 16 32 75 62, mail:

You can apply for this job no later than January 06, 2021 via the
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  • Employment percentage: Voltijds
  • Location: Leuven
  • Apply before: January 6, 2021
  • Tags: Computerwetenschappen

In your application, please refer to