🔬 I work on inverse problems for PDEs and machine learning, mostly in Julia: learned priors for inverse problems, and models that learn relations rather than functions.

• 🔁 Lenticulum.jl: learned relations instead of functions. One model answers a query in any direction (forward, inverse, mixed); inference is root-finding, backpropagation the implicit function theorem. Tutorials (also as Jupyter notebooks) · theory vault · references
• ⚡ EITDenoiser.jl: diffusion priors for Electrical Impedance Tomography, an ill-posed PDE inverse problem (Lux + Reactant + Enzyme).
• 🧱 ModularEIT.jl: an EIT library built from exchangeable parts (finite elements, electrode models, adjoint gradients, regularisers, fast linear solvers), with API docs and a theory wiki.
• 🕸️ Moonkale: a graph-native editor for knowledge and code, an experiment in building a larger application largely with AI.

🤝 Contributed to SciML/ReservoirComputing.jl (Wigner-initialised symmetric random matrices).

Julia (main). Some Python, Rust and C++. Lean 4 at the level of the Lean 4 game.

✅ I write code with AI assistants and treat correctness as my job: checks against closed-form solutions, honest baselines, and stated limitations.

📚 I think papers and books should be parsed into linked wikis: once LLMs remove the boilerplate between a DOI and the information you need, you can think about the subject instead of the path to it.

🌐 More at mathstruct.org.