Summer semester 2026

Lecture: Mathematical Modelling in Medicine

This course introduces mathematical modelling techniques for medical applications, with inverse treatment planning (ITP) in brachytherapy as a central example. The first part develops a model-based approach, deriving dose deposition models from radiation transport principles and formulating treatment planning as an inverse optimization problem, including objective functions, clinical constraints, and numerical methods.

The second part covers fundamentals of machine learning, focusing on neural networks such as convolutional networks and U-Net for medical image segmentation, and their integration into the ITP pipeline. Throughout, the course compares model-based and data-driven approaches, highlighting where machine learning is beneficial and where classical models remain essential, and concludes with an outlook on learning-based optimization.

The lecture is complemented by exercises.

Seminar: Information Geometry

Information geometry studies the geometric structure of families of probability distributions, providing a differential–geometric framework for statistics and machine learning. Statistical models are viewed as manifolds equipped with the Fisher–Rao metric and dual affine connections, linking statistics, optimization, and convex analysis. This perspective underlies methods such as natural gradient descent and divergence-based learning. The seminar introduces core concepts (statistical manifolds, Fisher information, dually flat structures), followed by selected advanced topics and applications in areas such as optimization, inference, and reinforcement learning.