I work on structure-preserving machine learning and numerical methods, leveraging differential geometry and mathematical physics.
Looking for an MSc thesis, and open to internships and collaborations in AI4Science and applied mathematics.
MaxwellGP: Gaussian Process for Maxwell's Equations
- [Paper] Gaussian Process for Source-Free Maxwell's Equations [in progress]
Research Assistant at the Seminar for Applied Mathematics (SAM), ETH Zurich
- Geometric field theory of electromagnetism on Lorentzian spacetime
- GP kernel built by applying spectral exterior calculus to the Hodge–Dirac equation
- Joint SIAM journal paper with Prof. Dr.-Ing. Stefan Kurz and Félix Lino Vittori
- [Semester Project] BEM Benchmark of the EPGP for Maxwell Cavity Scattering 2026
Supervised by Prof. Dr.-Ing. Stefan Kurz
- [Talk] Ψec: A Local Spectral Exterior Calculus 2026
Finite Element Exterior Calculus
- [Library] Formoniq: Structure-preserving FEEC engine in Rust [ongoing]
Coordinate-free PDE solving with differential forms on pseudo-Riemannian manifolds of arbitrary dimension
- Structure-preserving engine for the Hodge–Laplace and Hodge–Dirac operators
- Arbitrary dimension and form degree, with support for non-trivial topology
- Regge calculus for any metric signature: Riemannian and Lorentzian (spacetime)
- Discretization of the de Rham complex (nilpotency, cohomology, and Hodge decomposition)
- ~24k lines of pure Rust across 8 modular crates, each a self-contained math library
- Parallel solver toolchain in Rust (faer direct solves, rayon-parallel assembly)
- Began as the BSc thesis implementation, now a standalone library
- Live Demo: formoniq-studio.lwirth.com (WebGPU/WebAssembly)
- Repository: GitHub:formoniq, viewer at GitHub:formoniq-studio
- [Guest Lecture] Discretization of Differential Forms for the Numerical Solution of PDEs 2026
Given in the course "Electromagnetics and Differential Forms" (Prof. Dr.-Ing. Stefan Kurz)
- [BSc Thesis] Rust Implementation of FEEC on Coordinate-Free Simplicial Complexes 2025
"The best BSc thesis I have seen in years" — Prof. Dr. Ralf Hiptmair
- [YT Video] What is Finite Element Exterior Calculus? 2025
Proof Assistants & Type Theory
- [ZUCCMAP] Lean4 and the Curry–Howard Isomorphism 2024