Erik Löffelholz
Personal Profile & Research Interests
Mathematical Physics M.Sc. with a background in differential geometry, PDE theory and field theory, now working mainly on scientific software and machine learning. I am as comfortable with the maths as with the code: I have built differentiable physics simulators, graph generative models, and a discrete differential geometry library, most of it written from scratch in PyTorch. My recurring interest is how structured systems grow out of simple local rules.
Education
Research Experience
- Built GPU-accelerated tooling in PyTorch and Three.js for embedding discrete meshes into Riemannian manifolds (Euclidean, spherical and hyperbolic spaces) by spring-mass energy minimization with analytic differentials. This became the computational basis for our co-authored Bridges 2026 paper on illustrating hyperbolic surfaces.
- Implemented a discrete differential geometry library: cotangent Laplacians, mass matrices, Gaussian and mean curvature, heat-method geodesic distances, isotropic remeshing and dihedral-angle bending energy, running on CUDA, MPS and CPU.
- Developed Ricci-flow surface evolution and procedural strand and weave generation on curved surfaces using a half-edge mesh, with interactive 3D visualization.
- Wrote differentiable mesh-based physics simulators with a binary WebSocket protocol that streamed PyTorch state to the browser, roughly 10 to 20 times faster than JSON.
- Built a graph ML framework from scratch in pure PyTorch (no PyG or DGL) for generating 3D tree morphologies. It covers joint discrete-continuous diffusion and autoregressive spatial-tree VAEs over both graph topology and 3D node positions, evaluated with Sholl analysis and spatial MMD.
- Developed DiffQFT, a differentiable holographic QFT framework in Euclidean AdS2: Witten-diagram Monte Carlo integration through PyTorch autograd, neural surrogates, and a PINN for the Klein-Gordon equation.
- Implemented a PINN solver for ten classical PDEs, plus browser-based physics demos: a neural ODE that learns chaotic Lorenz dynamics from scratch, and a real-time particle and cloth simulation with an optional PyTorch backend.
- Work fluently with agentic coding models and LLM-assisted development.
- Write and review graduate-level mathematics, physics and science prompts and solutions for large-language-model training.
- Rate and compare model outputs (RLHF) for correctness, reasoning quality and helpfulness.
- Do coding and code-review tasks in Python, C++, JavaScript and front-end coding.
- Contribute German (de-DE) prompt and audio-prompt tasks.
Teaching & Academic Service
- Reviewed mathematics content for school textbooks, checking it for technical correctness and clarity.
Publications & Conferences
Fabian Lander, Erik Löffelholz, Diaaeldin Taha, Steve Trettel, Anna Wienhard.
"Illustrating Hyperbolic Surfaces with Mesh Embeddings."
Submitted to the Bridges Conference 2026 (Regular Papers Track). Under Review.
Relevant Skills & Languages
Programming
Python · JavaScript · TypeScript · C++
Machine Learning
PyTorch (Autograd, PINNs, GNNs) · Diffusion Models · VAEs · Neural ODEs
Scientific Computing
Numerical Integration (Runge-Kutta, Monte Carlo) · Differentiable Simulation · NumPy · SciPy
Mathematical Methods
Functional analysis · PDE theory · variational methods · differential geometry · discrete differential geometry · group theory
Tools & Workflow
Git · Docker · FastAPI · LaTeX · Agentic Coding Models · AI Data Labeling · RLHF / LLM Evaluation
Languages
German (native) · English (C1, full professional proficiency)
Referees
Dr. Diaaeldin Taha
Research Group Leader (Mathematical Structures in AI)
Max Planck Institute for Mathematics in the Sciences, Leipzig
taha@mis.mpg.de
Selected Projects
Full project portfolio with live demos at erik2810.github.io/projects