Are you excited about mathematics and motivated by real-world applications? Would you like to work at the interface of uncertainty quantification (UQ) and differential equations, where probability theory meets real-world applications in the framework of dynamical systems? Then, you should apply for this PhD position.

Project embedding

The dynamics of many real-world systems can be modeled in terms of differential equations, for example ocean circulations and Greenland Ice Sheet dynamics. Several such subsystems of the earth have been identified to be at risk of tipping, that is, undergoing drastic, abrupt, and oftentimes irreversible changes. This can happen when environmental conditions overshoot threshold values. From a mathematical point of view, these tipping phenomena can be considered as rather generic. They also occur in other fields such as neuroscience and ecology. When it comes to real-world applications, uncertainties, for example in terms of misspecifications of model parameters, need to be taken into account since they can crucially alter inherent tipping dynamics.

Project description

In this project, we will use an interdisciplinary approach to develop mitigation strategies against undesired abrupt changes (tipping) in complex systems. The idea is to combine aspects from nonlinear dynamics, in particular bifurcation theory, with methods from Uncertainty Quantification (UQ). We will investigate how control pathways under uncertainty --- that allow to restore the original stable state of a complex system --- can potentially be applied to complex systems such as the Atlantic Meridional Overturning Circulation or the Greenland Ice Sheet.

The research focus area will be at the interface of stochastics, numerical analysis for (stochastic) ordinary differential equations, and optimal control. Numerical algorithms and investigations will play a key role in solving the stochastic optimal control problems that arise.

Group embedding

You will be a member of the Centre for Analysis, Scientific Computing and Applications (CASA, see https://casa.win.tue.nl/home/). Within CASA, you will be part of the Computational Science group (see https://www.tue.nl/en/research/research-groups/mathematics/center-for-analysis-scientific-computing-and-applications/computational-science) that seeks to develop and apply methods aimed at accelerating large-scale computations and simulations of physical models while maintaining accuracy through model order reduction and scientific machine learning. The group also focuses on using these reduced order models in the context of UQ, where a connection to this project can be established.

It is not expected that you already have expertise in all of the above mentioned areas. You should, however, be interested in diving into these areas and learn more about them during your PhD. A successful candidate

• Holds (or be close to obtaining) an MSc degree in an (applied) mathematics program,
• Brings a very high motivation for the topic and to learn new material besides already existing expertise,
• Has a strong background in at least one of the following fields: probability theory, (numerical analysis for) ordinary differential equations, optimal control,
• Has programming experience in Matlab or Python,
• Is able to work in an interdisciplinary team,
• Is motivated to develop teaching skills and coach students,
• Is fluent in spoken and written English (C1 level).

We offer a meaningful job in a dynamic and ambitious university, in an interdisciplinary setting and within an international network. You will work on a beautiful, green campus within walking distance of the central train station. In addition, we offer you:

• Full-time employment for four years, with an intermediate evaluation (go/no-go) after nine months. You will spend 10% of your employment on teaching tasks.
• Salary and benefits (such as a pension scheme, paid pregnancy and maternity leave, partially paid parental leave) in accordance with the Collective Labour Agreement for Dutch Universities, PhD scale (min. €2,770 max. €3,539)
• A year-end bonus of 8.3% and annual vacation pay of 8%.
• High-quality training programs and other support to grow into a self-aware, autonomous scientific researcher. At TU/e we challenge you to take charge of your own learning process.
• An excellent technical infrastructure, on-campus children's day care and sports facilities.
• An allowance for commuting, working from home and internet costs.
• A Staff Immigration Team and a tax compensation scheme (the 30% facility) for international candidates.