PhD position on Uncertainty quantification in consumption patterns and flexibility of thermal loads

Katholieke Universiteit Leuven
October 22, 2022
Offerd Salary:Negotiation
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Working Time:Negotigation
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PhD position on Uncertainty quantification in consumption patterns and

flexibility of thermal loads

(ref. BAP-2022-627)

Last modification : Thursday, August 18, 2022

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 simulation, optimization, data science, uncertainty quantification and high performance computing. The present PhD fellowship is granted within the collaboration between NUMA (KU Leuven) and VITO. The successful candidate will be supervised by Prof. Dirk Nuyens (NUMA) and co-promoted by Dr. Brida Mbuwir (VITO).

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Advanced control strategies, and model predictive control (MPC) in particular, are gaining widespread interest for building climate control, since they can systematically save energy and/or costs with simultaneous thermal comfort improvement, as well as adapt the energy demand according to the available renewable/residual supply. MPC however suffers from (1) parametric uncertainties, which are uncertainties that can be decreased (though not fully eliminated) by adaptation improvement of model parameter (e.g., through learning), and (2) additive uncertainties (such as forecast uncertainty) that cannot be substantially decreased but that can be dealt with in the decision-making process. These substantially limit the performance of MPC approaches.

Several computational methods to handle uncertainties in mathematical models have recently been developed at NUMA; for example, quasi-Monte Carlo methods in forward uncertainty quantification for PDEs with random diffusion coefficients. Quasi-Monte Carlo methods are multivariate quadrature methods which are especially suitable for higher dimensional integrals/expectations, having the possibility of vanquishing the curse of dimensionality under certain conditions. These methods can also be used for inverse problems, such as determining parameters of a mathematical model given data, and for function approximation. In particular, Bayesian inversion allows the formulation of a point estimator for the parameters of a mathematical model in terms of (high- dimensional) integrals. If the mathematical model is relatively expensive then it can be approximated by a Gaussian process surrogate. The Gaussian process emulator can be interpreted as a kernel interpolation method for function approximation with added uncertainty. Recently new construction methods for quasi-Monte Carlo point sets for function approximation were developed which can also be used for kernel interpolation methods. Last but not least, in the dissertation of Van Barel at NUMA, multilevel Monte Carlo and quasi-Monte Carlo methods were developed for robust optimization under uncertainty.

In this PhD research, we aim to improve this methodology in direct, practical application to optimal control problems in residential and commercial thermal energy management.

  • You hold a Master of Science degree in electrical engineering, software engineering, computer science, mathematical engineering or data science.
  • You are proficient in English (oral and written) to allow effective communication.
  • Offer

    The location for this position will be Leuven (Departments of Computer Science) and Genk (EnergyVille). The successful candidates will receive:

  • Doctoral scholarships of four years, and a PhD degree in Engineering if successful
  • Multiple benets (health insurance, access to university infrastructure and sports facilities, etc.)
  • A very competitive salary, including social security
  • The opportunity to participate in research collaborations and international conferences
  • Both the city of Leuven, just 20 km east of Brussels, the heart of Europe, and the city of Genk, offer a stimulating, young and multicultural working environment
  • Interested?

    For more information please contact Prof. dr. ir. Dirk Nuyens, tel.: +32 16 37 35 59, mail: or Mr. Ward Melis, tel.: +32 16 32 06 16, mail:

    KU Leuven seeks to foster an environment where all talents can flourish, regardless of gender, age, cultural background, nationality or impairments. If you have any questions relating to accessibility or support, please contact us at

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