Gradient methods, such as gradient descent and stochastic gradient descent, achieve remarkable performances in neural network training but suffer typically from strong instability that makes the optimization of specific architectures challenging, time-consuming, and susceptible to attacks. For this reason, a dynamic regularization of the optimization algorithm is often necessary. Our goal is to lay a solid theoretical foundation able to unify different regularization strategies by looking at the gradient-flow structure of the training algorithm. We will use these theoretical insights to study sparsity properties of neural networks during training, analyzing how they depend on the chosen regularization. We will then develop a robustness theory for dynamically regularized neural networks able to explain and defend against adversarial attacks. Applications to biological data-driven models such as CT-reconstruction, single-particle tracking (SPT) for fluorescence microscopy and microbubbles flow for drug delivery 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) headed by Prof. Christoph Brune at the department of Applied Mathematics. There will be plenty of opportunities for collaborations with researchers in 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: optimization, theoretical machine learning, functional analysis, inverse problems, partial differential equations, numerical analysis, calculus of variations;
• You are interested in improving your coding/programming skills during the PhD;
• You are proficient in English.

• As a PhD student 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;
• An active research group, bridging applied and pure mathematics;
• 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 € 2.541,- (first year) to € 3.247,- (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;
• 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.