Errors that matter: Uncertainty-aware universal machine-learning potentials calibrated on experiments

Machine-learning models of atomic-scale interactions achieve the accuracy of the quantum mechanical calculations on which they are trained, but at a dramatically lower computational cost. Their predictions can be made trustworthy by uncertainty quantification techniques that estimate the residual error relative to their reference. These errors, however, do not include uncertainty contributions from the approximations inherent in the electronic structure calculations, which are often the main source of discrepancy with empirical observations. We construct an ensemble of ML potentials trained on multiple electronic-structure references and calibrate it against experimental data on cohesive energies, atomization energies, lattice constants and bulk moduli of simple materials and molecules, similar to the uncertainty-aware functional distribution approach. The resulting ensemble of models, which we call PET-UAFD, can be used to simulate matter across a wide range of compositions and thermodynamic conditions. By comparison with experimental measurements of the density and structure of liquids, we demonstrate that, even outside the static properties on which it was calibrated, PET-UAFD enables predictions that are as accurate against experiments as the best available electronic-structure reference and that the spread in the ensemble can be used to assess the reliability of such predictions. We also introduce the PET-EXP protocol that uses shallow ensembles and statistical reweighting techniques to provide accurate estimates of uncertainty relative to experimental measurements at virtually no additional cost over a simulation based on a single conventional ML potential. Ultimately, this approach provides a practical and inexpensive approach to elevate machine-learning potentials from faithful interpolators of approximate theories to genuinely predictive tools anchored in experimental reality.