Research

My current research focuses on deep Gaussian processes and how to apply them in Bayesian inverse problems. Such inverse problems arise, e. g., in image reconstruction.

Paper on Deep Gaussian Process Priors

We have now released the pre-print on our work with Deep GPs for Bayesian image reconstruction! Deep Gaussian processes are an intuitive way to model non-stationary data, such as images. That makes them a natural choice as a prior in Bayesian imaging tasks. But generating samples from the posterior is computationally challenging. We solve this by combining the stochastic PDE representation of Matérn-type GPs, rational approximation, and determinant-free MCMC. Check out our paper here:
https://arxiv.org/abs/2412.10248 (and code for all the experiments can be found here: https://github.com/surbainczyk/deep_gp_priors)

Master’s Thesis and First Paper

My master’s thesis at TU Munich was supervised by Dr Brendan Keith and Prof Barbara Wohlmuth. During that time, I worked on an algorithm that optimises the shape of a structure under load to minimise the strain energy in the presence of uncertain parameters. Working on my thesis exposed me to a large number of topics: stochastic optimisation, adaptive sampling, risk measures, shape optimisation, finite elements, linear elasticity, sequential quadratic programming, …
The main question it all boils down to is how many samples one needs at each iteration in an SGD-type algorithm (hence “adaptive sampling”). I handed in my master’s thesis in 2020 and stayed on for a few more months to contribute to a paper on adaptive sampling under constraints. The paper has now been published (open access!) and can be found here:
https://academic.oup.com/imajna/advance-article/doi/10.1093/imanum/drac083/6991354