Fidelity of Machine-Learned Potentials: Quantitative Assessment for Protonated Oxalate

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 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 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 vibrational self-consistent field/vibrational configuration interaction calculations using fitted dipole moment surfaces. In addition, tunneling splittings for the hydrogen transfer between two equivalent structures are reported using three different methods: ring polymer instanton theory, diffusion Monte Carlo simulations, and the Q i m -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.