TENKi: counting the value of borrowed knowledge to a materials campaign in measurements saved

Materials campaigns draw on data of very different cost: a band gap costs almost nothing from a database, core-hours from a hybrid-functional density functional theory (DFT) calculation, and instrument time from a measurement. No calibration carries values from low-cost to costly sources, and multi-fidelity methods do not state how many costly evaluations an imported ordering of the candidates replaces. We test whether that ordering, with its margins, reduces the evaluations needed to reach a given ranking quality, and whether the saving can be measured for each route. TENKi (Transfer-ensemble Knowledge Inheritance) records ranking agreement against budget while a ranking model is fitted to queries that order several candidates at once, with the donor ordering entered as a prior whose trust is learned from incoming results. The evidence is 261,053 archived band-gap records from eight sources, 171 semiconductors with gaps computed on demand, and an aluminium–magnesium–silicon (Al–Mg–Si) alloy pool computed with DFT and molecular dynamics. Queries ranking four candidates outperform pairwise comparisons on every source, a donor prior replaces nearly half of the early measurement budget, and a trained query-selection policy reaches the ranking quality of random selection with fewer evaluations on held-out sources, whereas hand-written rules do not. An ordering from the generalised gradient approximation cuts hybrid-functional compute about sixfold, while an archived ordering that lacks the alloys gives no saving at fixed trust; for Al–Mg–Si, a foundation-potential ordering lowers the DFT compute needed to find eight of the ten most stable compounds from 19% to 5%. The saving depends on direction and coverage, and the agreement-versus-budget curve separates disagreement that further sampling removes from gaps that remain, so a campaign can use these curves to decide which source to compute first, how far to trust it, and when further evaluations stop improving the ranking.