Research and Scientific works

Ongoing PhD in Scientific Machine Learning

PhD research in the Scientific Computing Division of Uppsala University (2024-) under the supervision of Prashant Singh in the Scientific Machine Learning group (results not yet published)

My Phd is focuses on enhancing scalability and understanding of large-scale optimization in inverse problems and machine learning models, particularly ill-posed non-convex optimization. The considered applications include simulation based inference for 1D-time series representing protein/mRNA copy numbers and microscopy images.

Master thesis (on diva)

I wrote my thesis at Uppsala University under the supervision of Prashant Singh and Aleksandr Karakulev on the topics of optimization for machine learning and inverse problems.

In my thesis I explored advanced techniques in supervised deep learning, focusing on how they can be applied to broader inverse problem settings. I evaluated Sharpness-Aware Minimization (SAM) combined with the Adam optimizer, showing that it can improve generalization and convergence in some cases. Additionally, I analyzed the concepts of flatness and sharpness in deep learning, validating results for path-norm and PAC-Bayes bounds but finding limitations with Hessian-based measures. My research highlights the potential applications of SAM in lower-dimensional problems and provides insights into its practical limitations.

BsC thesis (on university site - Hungarian)

I wrote my thesis at ELTE (Eötvös Loránd Tudomány Egyetem) under the supervision of Zoltán Blázsik in the Department of Mathematics on the overview of theory concerning the chordal graphs.

My bachelor’s thesis provides an overview of classical results on chordal graphs, also known as rigid circuit graphs. It begins by introducing key graph theory concepts, followed by an analysis of early characterizations of chordal graphs from the 1960s. I focus on the characterization based on minimal separator sets and simplicial ordering, the latter being foundational for efficient algorithms used to identify chordal graphs. This method also has practical applications, such as register allocation in compilers. The foundational algorithmic properties of chordal graphs are also discussed in the thesis. In addition, we explored subclasses of chordal graphs, including strongly chordal graphs, and conclude by examining leaf powers and their relevance in fields like evolutionary biology.