Differentiable, model-agnostic free energy calculation

Thomas D Swinburne, Mihai-Cosmin Marinica, Clovis Lapointe

Keywords: Phase diagram, Score Matching, Atomic Simulation, Fine tuning

TL;DR: Free energy calculation without a priori specification of an atomic interaction model, for UQ and fine-tuning to known phase boundaries

Abstract: The vibrational free energy is essential to predict finite temperature material properties. Current methods employ slow, largely sequential sampling with a fixed machine learning interatomic potential (MLIP) to satisfy the tight 1-2meV/atom (1/40-1/20 kcal/mol) convergence requirements. Forward or back propagation of MLIP parameters is not practically possible, meaning estimates cannot be used in objective functions for alignment to reference data or distillation. For the broad class of generalized linear MLIPs we show free energies can be cast as the Legendre transform of a high-dimensional descriptor entropy, accurately estimated via score matching. Our main result is a model-agnostic estimator which returns meV/atom accurate, end-to-end free energies as a function of MLIP parameters. Sampling is efficient and highly parallel, requiring 10x fewer force calls and 100-1000x less walltime than a single thermodynamic integration estimate. Tensor compression allows lightweight storage and inference is instantaneous. In forward propagation, a single estimator predicts a broad ensemble high temperature thermodynamic integration calculations for W. In back-propagation, we fine-tune the $\alpha-\gamma$ transition temperature in an Fe model from 2000K to 1063K, a first demonstration of MLIP alignment against known phase boundaries.

Submission Track: Paper Track (Short Paper)

Submission Category: AI-Guided Design

Institution Location: USA and France.

Submission Number: 55