materials simulation developers

Abstract: Universal machine learning force-field generalization to multicomponent environments generated by compositional design remains insufficiently assessed. We construct a benchmark of 7,599 multicomponent configurations inspired by high-entropy design, elemental substitution and anion mixing. Eleven pretrained models are evaluated against density functional theory for energies, forces and stresses, with assessment extended to elastic, vibrational and adsorption-related properties. Force errors are analysed through training-reference coverage, local geometric heterogeneity, distance directionality and elemental response. Distances to training-reference environments reveal a qualitative association between coverage differences and increasing errors, while substantial variation remains at similar distances. Higher-error groups show greater local geometric heterogeneity, although OMat24 provides broad coverage of these environments. Relative to training-reference pair medians, errors remain low near the median, rise steeply on the compression side and increase more weakly on the extension side. After matching element pairs and absolute distance deviations, compression-side force errors are 1.81-1.95 times extension-side errors. Model-predicted pairwise interaction curves show greater curvature under compression. Fitting difficulty in independent elemental systems correlates with electronic band-energy responses to atomic displacements and Fermi-level shifts, and a similar pattern is observed in multicomponent systems. In parameter-matched comparisons, spherical-harmonic representations with maximum degrees of 2 and 4 lower test force errors for 38 and 40 of 43 elements, respectively, while differences in elemental difficulty remain. These findings inform force-field selection for experimental compositional design and identify targets for training-data sampling and model representations.

Abstract: Phase-field trajectories governed by the Allen--Cahn equation determine the effective force $G=F'/\eps^2$, but not the free-energy potential $F$ and interfacial scale $\eps$ separately. We introduce surface-tension-calibrated Allen--Cahn identification (STAC), a two-step method that resolves this ambiguity using an independently supplied surface tension. First, space--time weak moments produce a linear inverse problem without differentiating the measured field. A Bernstein representation with positive coefficients enforces two stable pure phases and a single central energy maximum. Second, the surface tension fixes the remaining scale algebraically. We prove scale equivalence of the forward model, uniqueness of the calibrated pair within this class, and finite perturbation bounds that remain valid when the potential vanishes at the pure phases. Experiments with resolved synthetic phase fields separate the effects of the structural constraint, ridge regularization, and constitutive approximation error. Across 80 shared noisy records, unconstrained degree-five regression produces six potentials with an incorrect well structure. Positivity combined with ridge regularization eliminates these violations and reduces the mean force error from 8.70\% to 5.66\%. Lower-degree models are nevertheless more accurate in some tests, and an admissible law outside the positive Bernstein family shows how the constraint can introduce approximation bias. STAC thus recovers a structurally admissible, physically scaled potential while making explicit which information comes from the observed dynamics and which comes from the independent surface-tension datum.