Machine-learned interatomic potentials with calibrated, guaranteed error bounds outside the training distribution

• Heuristic uncertainty. Deep ensembles, dropout, last-layer Bayesian and Gaussian-process-style approaches, and committee disagreement are standard for active learning. Comparative studies find ensembles generally calibrate better than single-network Bayesian approximations but cost several-fold more and are overconfident under distribution shift (Farris et al., arXiv:2509.19180; Kurniawan, Wen and Tadmor, arXiv:2508.06456).
• Conformal and learned perturbations. Conformal prediction gives marginal coverage for exchangeable data only; learned functional-perturbation approaches are the topic of recent preprints (Zaghen et al., arXiv:2605.19939, 2026).
• Foundation potentials. Models such as MACE-MP-0, UMA and Orb give accurate average-case results on in-domain benchmarks (Matbench Discovery; OMol25 evaluations) but no per-structure certificate; documented failure modes include systematic softening of the PES (Deng et al., npj Comput. Mater. 2025) and degraded extrapolation to high-energy or out-of-domain structures.
• Not shown. No published MLIP offers distribution-shift-robust coverage guarantees validated on chemically held-out data together with MD-trajectory error control, to the knowledge of this entry.

Trustworthy MLIPs allow ab initio-quality simulation to be automated in drug discovery, battery electrolytes, catalysis and crystal structure prediction without re-validating against DFT at every step; error bars on predictions would make results publishable and auditable.

A method whose coverage is demonstrated at the stated level on pre-registered out-of-distribution splits (including at least one chemically held-out split of OMol25 or an equivalent) and in long MD runs, with ablations against ensembles, reproduced independently, plus (preferably) a proof of coverage under a stated shift assumption.