• Accepted Paper

Fidelity of machine-learned potentials: Quantitative assessment for protonated oxalate

Chen Qu, Paul L. Houston, Qi Yu, Apurba Nandi, Joel M. Bowman, Valerii Andreichev, Silvan Käser, and Markus Meuwly

PRX Intelligence - Accepted 2 September, 2026

DOI: https://doi.org/10.1103/jfjx-djk2

Abstract

There has been a veritable explosion of methods and software to perform machine-learned re- gression on datasets of electronic energies and forces to develop high-dimensional machine learned potential energy surfaces (ML-PESs). A major, but not deeply-studied aspect is how well different ML-PESs represent the same dataset on which they were trained, beyond the standard statistical precision measures. Here, this is examined using several “stress tests”, for two widely used machine- learned potential approaches. One is based on permutationally invariant polynomial (PIP) linear least square regression and the other is the message-passing neural network PhysNet approach. The energies from the two PESs are directly compared as are the IR spectra determined from VSCF/VCI calculations using fitted dipole moment surfaces. In addition, tunneling splittings for the hydrogen transfer between two equivalent structures are reported from using three different methods: ring polymer instanton theory, diffusion Monte Carlo simulations, and the Qim path method. These calculations require the evaluation of on the order of one billion energies that are widely dispersed in the 15-dimensional configurational space. The two PESs yield results for these quantities in excellent agreement with each other.

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