PhD Position in Constrained Optimization of Nonlinear Uncertain Systems Catholic University of Leuven Department of Computer Science

Project

Taking into account various forms of uncertainty is a common challenge in the design of industrial systems: there can be uncertainty on the physical parameters of the model, on the manufacturing process, and/or on the load conditions. At the same time, the solution to design optimization problems involves the numerical solution of partial differential equations, which are already computationally expensive even without uncertainty.

The goal of this thesis is to develop mathematical and numerical methods for solving large scale optimization problems featuring uncertainty. The most popular approaches today consist in replacing the objective and constraint functions by some statistically averaged quantities. In this thesis, we will develop more systematic methodologies for computing efficiently the statistics associated to the optima of a family of parameterized constrained optimization problems.  Several approaches will be explored:

• the development of reduced order methods for PDE-constrained optimization procedures with uncertainty
• the development of mathematical and numerical methods for optimization problems featuring many local constraints
• the use of stochastic consensus-based optimization methods for global optimization
• the use of neural networks rather than low rank methods as reduced order models

The methodologies will be tested on physical applications in the field of PDE constrained optimization, such as optimal control, topology and shape optimization of engineering systems, and/or molecular dynamics.

Profiel

• Candidates must hold a master’s degree in Mathematical Engineering, Applied Mathematics, or equivalent
• Candidates should have a solid background in mathematics (notably finite elements 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.

Aanbod

• 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 the aim is to start no later than October 1, 2022.

Interesse?

This position will be co-supervised by Prof. dr. Florian Feppon (who will join NUMA on October 1, 2022) and by Prof. dr. ir. Giovanni Samaey.

For more information please contact Prof. dr. Florian Feppon, tel: +33 6 48 92 76 75, mail: florian.feppon@sam.math.ethz.ch, or Prof. dr. ir. Giovanni Samaey, tel.: +32 16 32 75 58, mail: giovanni.samaey@kuleuven.be.

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