The efficiency–coverage trade-off of scientific priors in Bayesian search: a registered benchmark on metallic multi-element elasticity data

Scientific priors speed up Bayesian optimisation in materials discovery, but a prior that steers a small budget toward the materials it favours may miss those it disfavours. We measured this in a benchmark with a registered analysis plan: 7,020 searches (3,000 of them over 3,550 metallic multielement Materials Project structures), for the shear modulus and the specific Young’s modulus, with a historical prior and a composition-only elemental-modulus heuristic, each mixed into expected improvement search with a fixed weight β. Coverage was the recall of the half of the top-5% materials that the prior itself scores lowest. Coverage loss at moderate weight was detected in 4 of 6 prior–objective settings. The elemental heuristic reduced the restricted mean number of acquisitions to a top-1% shear-modulus material by 13.9 at β = 0.25 with no detected loss of coverage, but its shear-modulus form, applied to the specific modulus, lost 44.0% or more of the baseline coverage at every nonzero weight. A weight both beneficial and safe under the registered criterion existed in 3 of 6 settings (2 under a post hoc joint error control), never above β = 0.25, and depended on the safety margin and on curation. At β = 0.5, in 5 of 6 settings the weighted search found more top-5% materials in total but, by its estimates, fewer of those its prior disfavours (a loss detected in 3): the prior redirected the search rather than reducing its yield. Faster discovery alone therefore does not show that a search keeps what its prior disfavours.