Fidelity of Machine Learned Potentials: Quantitative Assessment for Protonated Oxalate

TL;DR

This study evaluates the accuracy and consistency of two machine-learned potential energy surface methods for protonated oxalate, using stress tests and vibrational calculations, demonstrating their high agreement across diverse properties.

Contribution

It provides a detailed quantitative assessment of the fidelity of two ML-PES approaches, including stress testing and vibrational analysis, for complex molecular systems.

Findings

The two ML-PES methods show excellent agreement in energy and IR spectra.

Vibrational energies and tunneling splittings are accurately predicted by both methods.

The study demonstrates the reliability of ML-PESs in high-dimensional quantum calculations.

Abstract

There has been a veritable explosion of methods and software to perform machine-learned regression 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 are trained, beyond the standard fitting precision metrics. Here, this is examined in detail using several ''stress tests'', for two widely applied 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. These potentials and dipole moment surfaces are used in VSCF/VCI calculations of vibrational energies and wavefunctions. The energies from the two PESs are directly compared as are the IR spectra. In addition, tunneling splittings for the hydrogen transfer between two equivalent structures are reported from using three methods: ring polymer instanton theory, diffusion Monte Carlo simulations, and the $Q_{im}$ 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.