Juan was a PhD student in our group at CASUS from 2020 to 2025. His research combined numerical analysis and machine learning, with a particular focus on introducing Sobolev cubatures to discretize Sobolev gradient flows in variational problems. This approach helps mitigate numerical stiffness, which is especially relevant in applications such as autoencoders and PINNs and autoencoders and PDEs with jump discontinuities. 

After completing his PhD in collaboration with TU Dresden, Juan continued his research at the Max Planck Institute CBG and is now a postdoctoral researcher at the Bavarian AI Chair for Mathematical Foundations of Artificial Intelligence at Ludwig-Maximilians-Universität München, led by Prof. Gitta Kutyniok.

Gentian was a PhD student in our group at CASUS from 2021 to 2025. Gentian Zavalani is a researcher specializing in numerical analysis, with a focus on solving partial differential equations and performing numerical integration on complex geometries, particularly smooth surfaces. His work combines numerical methods with differential geometry to develop accurate and efficient algorithms for geometric computations, such as curvature estimation and high-order surface integration. Key contributions include global polynomial level set parametrizations, high-order integration techniques on triangulated surfaces, and error analysis of numerical schemes. He is currently a member of Prof. Oliver Sander's chair of Numerical Methods of Partial Differentiual Equations, Technical University Dresden (TUD).  

Janina was a PhD student in our group at CASUS from 2022 to 2026. Janina Schreiber is a researcher specializing in black-box optimization and surrogate modeling, with a particular focus on polynomial surrogate models for optimization and landscape analysis. Her work combines numerical approximation, sensitivity analysis, and evolutionary optimization to develop efficient methods for computationally expensive optimization problems. Key contributions include Polynomial-Model-Based Optimization (PMBO), polynomial-informed initialization of CMA-ES, and the use of polynomial surrogate models for sensitivity and landscape analysis.

Chethan completed his master’s thesis under our joint supervision at CASUS in 2023. Chethan Krishnamurthy Ramanaik is a researcher specializing in machine learning, with a particular focus on generative AI, autoencoders, and adversarial robustness. His work explores the preservation of topological structures in learned representations, the fairness and robustness of variational autoencoders, and the vulnerability of vision-language models. He is currently a research associate at the Research Institute CODE and the Chair of Open Source Intelligence at the University of the Bundeswehr Munich.