FEMMI

Finite Element Mass Map Inversion — a P3 finite-element / boundary-element pipeline for reconstructing the projected mass (convergence, \(\kappa\)) of a lens from weak-lensing shear, with a differentiable forward operator that powers both MAP reconstruction and full posterior uncertainty quantification.

Why FEMMI

• Catalog-native. FEM nodes are placed at galaxy positions, so the data term is evaluated exactly where you have measurements — no gridding/binning of the shear before inversion.
• Symmetric FEM–BEM coupling. The exterior mass-sheet mode is handled with a Steinbach Steklov–Poincaré coupling; the forward runs in float64 where it needs the precision to converge.
• A menu of priors. Wiener (default), total-variation, sparsity, maximum entropy, and a learned neural score prior (Remy et al. 2020) — all behind one interface.
• Uncertainty, not just a point estimate. Exact perturb-and-MAP for the Gaussian posterior and the paper's annealed HMC for non-Gaussian/neural priors, exploiting the differentiable forward.
• One config, one command. femmi run --config my_run.yaml describes the whole pipeline (forward, data, inverse, prior, sampler, output).

Next steps

• Installation
• Quickstart — reconstruct a map in a dozen lines
• Configuration & CLI — the femmi run workflow
• Priors & sampling — choosing a prior, auto-calibrated UQ
• Neural prior — training and using the learned score prior

The mathematical foundations (weak-lensing forward model, FEM–BEM coupling, regularization, sampling) are documented in MATH.md.