Decision-Time Representations in Closed-Loop Bimetallic Nanoparticle Design

Bimetallic core--shell nanoparticles are used across catalysis, plasmonics and energy storage because pairing two metals lets composition, size and morphology tune performance independently of either constituent alone. Machine-learned interatomic potentials have made it practical to relax and label large numbers of such particles computationally, motivating closed-loop design pipelines in which a surrogate model proposes new candidates for evaluation. Every such loop must select a candidate before it exists, so the surrogate can condition only on the variables used to specify a structure --- nuclearity, composition, morphology --- rather than on the geometry the particle actually adopts once relaxed. We quantify this representation gap on a Pd--Pt core--shell design campaign, extended to six further bimetallic pairs, comparing surrogate accuracy, acquisition performance and a physically motivated size-scaling law under matched cross-validation with paired bootstrap significance testing. Descriptors of the relaxed structure predict both formation energy and elastic stiffness substantially better than the pre-relaxation specification, and the gap persists across six regression families spanning kernel, linear and tree-ensemble estimators, so changing the feature set moves accuracy far more than changing the model family does. Consistent with that, five acquisition strategies conditioned on the weaker representation reach the pool optimum only one to two evaluations before the random-selection median, well inside the spread random draws show on their own, and the choice of input coordinate outweighs the choice of estimator. A rule-of-mixtures picture for composition-dependent stiffness fails once tested against the classical Voigt--Reuss bounds, pointing instead to a finite-size surface-softening effect shared by the energetic and elastic properties. A graph-propagation baseline built on the same atomic connectivity underperforms simple hand-built structural descriptors, showing that the gap closes with which statistics of the relaxed structure are computed rather than with representing the bonding graph itself. We recommend reporting this structure-conditioned fit routinely: it costs nothing beyond data already collected, and it quantifies the predictive headroom inaccessible to the pre-relaxation representation a design loop must otherwise rely on.