We are looking for a talented, research-oriented PhD candidate to join the project "Curve Ensemble Gradient Descents for Sparse Dynamic Problems".

Optimization methods in the space of measures have seen a dramatic increase in popularity in recent years. This is largely due to two factors: their connections with Optimal Transport (OT) and Wasserstein Gradient Flows, and their applicability to solve inverse problems and design infinite-dimensional machine learning algorithms.

The goal of this project is the analysis of dynamic optimization problems for time-dependent measures, where motion is governed by the penalization of OT energies. We plan to adopt a sparse perspective, analyzing how collections of trajectories can be employed to approximate dynamic distributions and how gradient descent methods in the space of curves can be used to achieve this goal. A full understanding of these dynamic problems and their efficient optimization is essential to address a wide class of inverse problems and machine learning methods. In particular, applications to single-particle tracking (SPT) for fluorescence microscopy and neuralODEs training will be considered.

The PhD candidate will work under the supervision of Dr. Marcello Carioni and will be part of the group “Mathematics of Imaging and Artificial Intelligence” (MIA) at the Department of Applied Mathematics. There will be plenty of opportunities for collaboration with researchers in the group of Prof. Carola Schönlieb at the University of Cambridge and in the group of Prof. Kristian Bredies at KFU Graz.

• You have, or will shortly acquire, an MSc degree in Mathematics;
• You have a solid theoretical foundation in one or more of the following topics: continuous optimization, functional analysis, optimal transport, inverse problems, partial differential equations, calculus of variations;
• You are interested in improving your coding/programming skills during the PhD;
• You are proficient in English.

• As a PhD candidate at UT, you will be appointed to a full-time position for four years, with a qualifier in the first year, within a very stimulating and exciting scientific environment;
• The University offers a dynamic ecosystem with enthusiastic colleagues;
• Your salary and associated conditions are in accordance with the collective labour agreement for Dutch universities (CAO-NU);
• You will receive a gross monthly salary ranging from € 2.770,- (first year) to € 3.539,- (fourth year);
• There are excellent benefits including a holiday allowance of 8% of the gross annual salary, an end-of-year bonus of 8.3%, and a solid pension scheme;
• The flexibility to work (partially) from home;
• A minimum of 232 leave hours in case of full-time employment based on a formal workweek of 38 hours. A full-time employment in practice means 40 hours a week, therefore resulting in 96 extra leave hours on an annual basis;
• Free access to sports facilities on campus;
• A family-friendly institution that offers parental leave (both paid and unpaid);
• You will have a training programme as part of the Twente Graduate School where you and your supervisors will determine a plan for a suitable education and supervision;
• We encourage a high degree of responsibility and independence, while collaborating with close colleagues, researchers and other staff.