The sparse grid combination method combined with multi-grid approach and deep learning

My name is Anna Clevenhaus and I am a third year PhD student in the Applied Mathematics and Numerical Simulation (AMNA) group at the University of Wuppertal, Germany. My interest in numerical simulations and analysis started during my bachelor studies. After that, I started the international curriculum of computer simulation in science. For my master thesis, I investigated European option pricing with the Heston model extended by a stochastic correlation process, using implicit schemes with alternating direction to solve the resulting partial differential equation.

Why I became a PhD student in the AMNA group
During my master’s degree, I had the opportunity to directly compare work in a research area with real-world applications. Therefore, the decision between a PhD and working in industry was easy for me. I applied for a PhD position and was happy to get the PhD position in the AMNA working group, which I was already familiar with through my Master’s thesis.

What I will do during my PhD
After focusing on financial modeling in my master’s thesis and the first two years of my PhD, my focus is changing to computer science. Since the combination of the sparse grid combination technique and the parareal algorithm is almost done, the next step is to extend the parareal algorithm to a multi-grid approach that takes advantage of the properties of the combination technique for a multi-dimensional application. To extend my modeling expertise, the application will be a physical one instead of a financial one. Other interesting topics I will be working on during my PhD are extrapolation and deep learning approaches using the sparse grids as the underlying grid structure.

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