Reference-free certification of machine-learning interatomic potentials
Abstract
Universal machine-learning interatomic potentials now reach held-out energy and force errors so small that they no longer predict how a model behaves in simulation. Here we show that a potential can be graded without any reference calculation, against properties the exact Born-Oppenheimer surface satisfies by mathematical or physical necessity. We organise these properties into four families, symmetry and invariance, self-consistency and integrability, statistical-mechanical equilibrium and regularity, and turn them into fourteen inexpensive probes, each certifying against a target that is exact and independent of chemistry and reference method. Every probe therefore returns an absolute, architecture-comparable score from the energies, forces and stresses a potential already exposes, and reveals failures a fixed test set cannot. Applied to 64 pretrained potentials, the suite resolves two orders of magnitude of certified quality at comparable reported accuracy, and flags a fine-tuned potential whose reference errors improve while its surface degrades until molecular dynamics fails. An interactive leaderboard of all 64 models is available at https://jhaens.github.io/pescert-bench.
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BibTeX
@misc{hanseroth2026referencefree,
title = {{Reference-free certification of machine-learning interatomic potentials}},
author = {Jonas Hänseroth and Christian Dreßler},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.00585},
eprint = {2610.00585},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.00585},
}
RIS
TY - UNPB
TI - Reference-free certification of machine-learning interatomic potentials
AU - Jonas Hänseroth
AU - Christian Dreßler
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.00585
UR - https://arxiv.org/abs/2610.00585
AB - Universal machine-learning interatomic potentials now reach held-out energy and force errors so small that they no longer predict how a model behaves in simulation. Here we show that a potential can be graded without any reference calculation, against properties the exact Born-Oppenheimer surface satisfies by mathematical or physical necessity. We organise these properties into four families, symmetry and invariance, self-consistency and integrability, statistical-mechanical equilibrium and regularity, and turn them into fourteen inexpensive probes, each certifying against a target that is exact and independent of chemistry and reference method. Every probe therefore returns an absolute, architecture-comparable score from the energies, forces and stresses a potential already exposes, and reveals failures a fixed test set cannot. Applied to 64 pretrained potentials, the suite resolves two orders of magnitude of certified quality at comparable reported accuracy, and flags a fine-tuned potential whose reference errors improve while its surface degrades until molecular dynamics fails. An interactive leaderboard of all 64 models is available at https://jhaens.github.io/pescert-bench.
ER -