About me

I am a postdoctoral researcher at the Technical University of Berlin in the research group Differential Equations, headed by Prof. Dr. Etienne Emmrich.

From March through September 2026, I am a Distinguished Fellow at George Mason University (Fairfax, VA, USA), hosted by Prof. Dr. Harbir Antil.

Previously, I held a postdoctoral position at the University of Freiburg, where I also completed my PhD under the supervision of Prof. Dr. Michael Růžička. From July 2023 to April 2024, I was a Walter Benjamin Fellow of the German Research Foundation (DFG), conducting research on numerical methods for so-called smart fluids in collaboration with Prof. Dr. Luigi C. Berselli at the University of Pisa.

Research profile

My research focuses on the numerical analysis of nonlinear PDEs and nonsmooth variational problems. I combine nonlinear functional analysis, convex duality, and structure-preserving discretisation to develop reliable approximations, computable error estimates, and efficient nonlinear solvers.

Two closely connected areas form the core of my work:

• Duality-based numerical methods. I use continuous and discrete convex duality to derive primal-dual error identities for a priori and a posteriori analysis, adaptive refinement, and error control for iterative solvers. My work includes explicit flux reconstructions and robust solvers based on semi-implicit gradient flows and prox-based semismooth Newton methods. Applications include obstacle and Signorini problems, TV minimisation, optimal insulation, and digital twins for structural health monitoring. Current directions include subgradient flows, higher-order discretisations, PDE-constrained optimisation, and learning-enhanced iterative solvers.
• Analysis and numerics of non-Newtonian and smart fluids. I develop existence theory for nonlinear flow models and establish convergence and error estimates for finite element and discontinuous Galerkin approximations. My work includes variable-exponent and micropolar fluids, evolution equations in time-dependent energy spaces, and generalised pseudomonotonicity methods. Current research extends this analysis to fully coupled smart-fluid systems, particularly chemically reacting fluids and models of synovial lubrication.

Two further directions complement this programme:

• Neural approximation of parametric PDEs. I study neural approximations of parameter-to-solution maps and their mathematical error analysis. Building on best-approximation results and a priori estimates for the Deep Ritz method, current work couples variational energies with physics-informed residuals for parametric p-Stokes systems, including parameter-dependent material laws, forcing, and geometries.
• Quantum-hydrodynamic generative modelling. I develop PDE-based generative methods using Schrödinger dynamics and their Madelung formulation. The initial phase is determined through PDE-constrained optimisation so that the resulting deterministic dynamics transport a reference distribution towards a prescribed target. Further research addresses scalable phase identification, structure-preserving discretisations, and error control.