Score matching the descriptor density of states for model-agnostic free energy estimation

Vibrational free energy estimation is a cornerstone of atomic simulation, essential to predict finite-temperature material properties. Expressing the free energy as a function of interatomic potential parameters is actively sought in modern workflows for uncertainty quantification or inverse design. However, to achieve meV/atom accuracy, existing schemes conduct slow, sequential sampling with fixed potential parameters. We present a solution, an efficient model-agnostic free energy estimator which is meV/atom accurate over a broad, multi-element parameter range. For a broad class of machine learning potentials we show the free energy is the Legendre transform of an entropy function, accurately estimated via score-matching. Sampling requires 10× less effort than a single traditional estimate, tensor compression ensures lightweight storage, and inference is instantaneous. We demonstrate targeting of phase boundaries in back-propagation, fine-tuning the α - γ transition temperature in a Fe model from 2030 K to 1063 K. Extensions to a range of high-dimensional integration tasks are discussed.