PhD Position in Topology Optimization of uncertain Physical Systems

Catholic University of Leuven Department of Computer Science

At the Department of Computer Science of KU Leuven, the Numerical Analysis and Applied Mathematics research unit NUMA works on numerical methods, algorithms and software for simulation and data analysis, with applications in many fields in science and engineering. The research in NUMA focuses, amongst others, on numerical simulation, optimization and high performance computing.


Topology Optimization (TO) is a powerful technology which allows to compute optimized designs of physical systems  in a fully automated manner, without any assumed parameterization of the geometry. From the mathematical standpoint, it consists of solving nonlinear optimization problems constrained by partial differential equations. This technology allows to improve the performance in various physical settings such as structural design, heat exchangers, or nanophotonic crystals.

In many industrial problems, the optimized design need to be robust with respect to various forms of uncertainties coming e.g. from the load conditions or from the manufacturing process. The optimized design needs to perform well in a continuum of (many) possible scenarios. This is especially challenging because solving physical models for all these possible situations (and accounting them in the optimization program) is not computationally tractable for realistic problems.

The goal of this PhD thesis is to develop efficient methods for taking into account arbitrary sources of uncertainties in Topology Optimization problems. A particular focus will be given on the treatment of uncertainties present in the optimization constraints, and on the use of efficient low-rank methods for capturing uncertainty.  The work will involve a good balance between  rigorous mathematical analysis and numerical implementation.


  • Candidates must hold a master’s degree in Mathematical Engineering, Applied Mathematics, or equivalent.
  • Candidates should have an excellent background in mathematics (notably finite elements methods  and numerical optimisation).
  • Candidates should have experience with scientific programming and the will to use  it as a daily and powerful research tool (python)
  • Excellent proficiency in English is required, as well as good communication skills, both oral and written.


  • A high-level and exciting international research environment.
  • A supportive and collaborative team in which you can develop know-how and expertise in state-of-the-art simulation methods.
  • The opportunity to build up research and innovation skills that are essential for a future career in research and development, both in an industrial and academic context
  • A competitive salary and travel funding
Applications will be continuously evaluated upon submission until a suitable candidate is selected.  The vacancy will remain open until a suitable candidate is selected. The starting date will be agreed upon between candidate and promotors but should be no later than October 1, 2023.


For more information please contact Prof. dr. Florian Feppon, mail:

You can apply for this job no later than February 15, 2023 via the
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  • Employment percentage: Voltijds
  • Location: Leuven
  • Apply before: February 15, 2023
  • Tags: Ingenieurswetenschappen
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