Enhanced WENO Shock-Capturing Schemes with Deep Learning

My name is Tatiana Kossaczká and I am a first year PhD student in the Applied Mathematics and Numerical Simulation (AMNA) group at the University of Wuppertal, Germany.
I completed my bachelor degree at the Comenius University in Bratislava (Slovakia). Then I continued with my studies at University of Wuppertal with the main focus on numerical analysis and computational finance. In my Master’s thesis I considered various problems from financial mathematics and applied the weighted essentially non-oscillatory (WENO) method for solving these problems.

Why I became a PhD student in the AMNA Group

During my studies I had some opportunities to work in the industry. Taking that experience into account I realized that I would like to spend some more time researching in the area that interested me. I was very happy to get the opportunity to do this at the AMNA working group, where I also worked during my Master’s studies.

What I will do during my PhD

My main focus during my studies was financial mathematics and computational finance. Therefore I thought I would continue to do the research in that area. Moreover, I got really familiar with the WENO method during writing my master thesis and wanted to focus on studying and improving this method. Recently, machine learning became very popular also in the applications of numerical analysis. I started to think about how to improve the WENO method via deep learning and got some ideas which I tried. As I continued with the experiments on enhancing this method I realized that I also want to apply my findings in the area of hyperbolic conservation laws, where this method actually comes from. This gave me a great opportunity to broaden my research horizons.

I am currently working also on enhancement of this method in the field of nonlinear degenerate parabolic equations. Although I spent the most of my research time in these two areas, I am still thinking about how to bring my findings into the branch of computational finance. Later in my PhD studies I would like to gain more experience with deep learning in numerical analysis as I was really enjoying to explore this new subject field.

Best regards
Tatiana Kossaczká