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

TD Swinburne and C Lapointe and MC Marinica, NATURE COMMUNICATIONS, 17, 248 (2025).

DOI: 10.1038/s41467-025-66938-8

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 10x 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 alpha - gamma transition temperature in a Fe model from 2030 K to 1063 K. Extensions to a range of high-dimensional integration tasks are discussed.

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