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 embeddingThe 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 descriptionIn 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 embeddingYou 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.