MetaXfam22: a 22-family de-confounded benchmark for cross-family generalization of metamaterial homogenization surrogates (code, data and manuscript)

MetaXfam22 is a benchmark for studying how the choice of training families affects thecross-family generalization of machine-learned surrogates for metamaterial homogenization. It contains 22 parameterized unit-cell design families, 600 cells each at 48x48resolution, with the full effective stiffness tensor computed by validated 2D numericalhomogenization (Q4 elements, periodic boundary conditions, plane strain, E_solid = 1,nu = 0.3, void E = 1e-6). Three controls distinguish it from earlier datasets. Solid fraction is rejection-sampledinto a common band [0.45, 0.75] and then histogram-matched across families, socross-family error is topological rather than a density extrapolation. Every cell isrequired to percolate in both directions under periodic boundary conditions, which removesnon-percolating cells whose stiffness is the void stiffness and whose anisotropy ratio isa quotient of two numerical zeros. Anisotropy is sampled continuously over sixteendistinct levels from 0 to 0.77 and in both signs (C11 > C22 and C22 > C11), and isdecoupled from topology class: the most anisotropic family is a perforation and the secondis a strut network. The record also contains the validated homogenization solver and its test suite, thefamily generators, a library of nine cheap training-set selection criteria (includingmaximum mean discrepancy and sliced-Wasserstein baselines from the domain-generalizationliterature), a from-scratch NumPy convolutional network, every analysis script, and thecomplete per-subset results as JSON so that new selection criteria can be scored againstthe full oracle without recomputation. Accompanying manuscript: "Which Families Should You Train On? Training-Set CompositionDominates Cross-Family Generalization of Metamaterial Homogenization Surrogates". Working repository: https://github.com/davidmashiah/metaxfam22