Deep learning of priors for Bayesian inverse problems in image analysis

Computer scientist Bastian Goldlücke and mathematician Stefan Volkwein have been working on algorithms for deep learning. At first, they worked with imaging, where an image restoration or reconstruction problem is replaced with deep neural networks trained (unsupervised) on the respective distributions. They then focused on how deep learning methods can be successfully combined with partial differential equations (PDE) to solve constrained optimization problems. Goldlücke says: “We observed that these classes of problems are highly relevant in real applications, including pandemics and electromobility, where networks consisting of different models have to be optimized, but the parameters of the models are uncertain.” Moving forward, they are interested in developing their research into teaching content and working on new methods for research within the cluster.