Uncertainty-Gated Escalation for a Solver-in-the-Loop Molecular Surrogate

Screening molecular candidates with a cheap surrogate is useful only if likely failures can be identified and selectively escalated to an expensive reference method. We formulate this deployment problem as fixed-budget verification and evaluate uncertainty by the error it removes, rather than by ranking quality alone. Specifically, we decompose the realized error removal as $R_b=C_b\eta_b$, where $C_b$ is the error concentration recoverable by an oracle budget of size $b$ and $\eta_b$ is the efficiency with which an uncertainty score recovers that oracle mass. This separates the opportunity for verification from the quality of uncertainty-based allocation. We study this framework in a controlled comparison between a solver-in-the-loop molecular surrogate and a conventional interatomic potential with matched equivariant backbone architectures. On an $8{,}000$-structure held-out set, escalating the $2\%$ most uncertain structures with the same feature-based score removes $29.6\%$ of the solver-in-the-loop model's total force-error mass but only $10.4\%$ of the interatomic potential's. Their selection efficiencies are similar ($75.1\%$ versus $69.8\%$), whereas their oracle-recoverable error concentrations differ substantially ($39.4\%$ versus $14.9\%$). Across the low-overhead uncertainty estimators considered, we do not establish an architecture-level advantage in ranking quality. These results show that uncertainty quality and verification value are distinct: under a fixed budget, operational value depends jointly on how errors are distributed and how effectively uncertainty identifies them.