Method & caveats

Each MLIP relaxes the bulk cell + ions to its own equilibrium lattice, builds a fixed integer supercell (perpendicular min-image ≥ 12 Å), then relaxes the perfect and each one-atom-removed supercell at fixed cell, ions only (ASE; BFGS for the variable-cell bulk pre-relax, FIRE for the supercells; fmax = 1e-2 eV/Å). The constant-volume formation energy is E_f = E_vac − (N−1)/N·E_bulk, computed per symmetry-inequivalent site (SOAP r_cut = 8 Å enumeration, with a spacegroup-locked Wyckoff cross-check). A row is done only if all three feeding relaxations converged. No DFT was computed in this campaign, so the headline Consensus MAE is the median |E_f − per-site cross-potential median| (eV) — it ranks "most typical", not "most correct". Read it alongside two external overlays, both phase-gated to the corpus ground state: vs PBE-DFT (published values from Medasani et al. 2015, 24 metals — the closest like-for-like comparand, since the MLIPs are PBE surrogates) and vs experiment (15 metals). The models reproduce PBE DFT to ~0.05–0.1 eV; the larger experiment gap on noble metals is mostly inherited from PBE itself. High-energy polymorphs are included (toggle "All polymorphs") but stress both the relaxers and the consensus, so the default view is ground states. Full protocol, the SOAP method note, the blow-up handling and the per-element DFT + experimental references (with citations and links): Vacancy-formation methodology →.