© private

Name: Oskar BROUKAL
Current position: Master student
Supervisor: Prof. Michael FEISCHL

Many applications involve uncertainties regarding the input data, such as material properties. These can be modeled using partial differential equations with random coefficients. A well-studied model here are diffusion equations with log-normally distributed diffusion coefficients. This means that the permeability of the material is random, and the logarithm of the permeability follows a Gaussian normal distribution. 

In my thesis, I am dealing with an extension of this problem to a new class of random coefficients and numerical methods for solving these. This new class of coefficients is called "Deep Gaussian Processes" and is inspired by deep neural networks. Roughly speaking, one constructs random coefficients whose probability distribution depends on other random coefficients. These processes model materials that are very inhomogeneous in some places but very homogeneous in others. For me personally, this topic is particularly exciting because it brings together many elements from different areas of mathematics. 

My biggest goal is to write a mathematically rigorous and sophisticated thesis. Since, in my experience, the supervision at the ASC is very good, I am confident that nothing stands in the way of this. What comes after the Master's is still unclear, but I am certain that I will be able to make good use of the mathematical skills and knowledge gained at TU Wien!

Further information: CV – Oskar BROUKAL, opens an external URL in a new window