Predicting hot-electron free energies from ground-state data

Machine-learning potentials are usually trained on the ground-state,\nBorn-Oppenheimer energy surface, which depends exclusively on the atomic\npositions and not on the simulation temperature. This disregards the effect of\nthermally-excited electrons, that is important in metals, and essential to the\ndescription of warm dense matter. An accurate physical description of these\neffects requires that the nuclei move on a temperature-dependent electronic\nfree energy. We propose a method to obtain machine-learning predictions of this\nfree energy at an arbitrary electron temperature using exclusively training\ndata from ground-state calculations, avoiding the need to train\ntemperature-dependent potentials, and benchmark it on metallic liquid hydrogen\nat the conditions of the core of gas giants and brown dwarfs. This work\ndemonstrates the advantages of hybrid schemes that use physical consideration\nto combine machine-learning predictions, providing a blueprint for the\ndevelopment of similar approaches that extend the reach of atomistic modelling\nby removing the barrier between physics and data-driven methodologies.\n