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We present a $\Delta$-machine learning model for obtaining Kohn-Sham accuracyfrom orbital-free density functional theory (DFT) calculations. In particular,we employ a machine learned force field (MLFF) scheme based on the kernelmethod to capture the difference between Kohn-Sham and orbital-free DFTenergies/forces. We implement this model in the context of on-the-fly moleculardynamics simulations, and study its accuracy, performance, and sensitivity toparameters for representative systems. We find that the formalism not onlyimproves the accuracy of Thomas-Fermi-von Weizs{\"a}cker (TFW) orbital-freeenergies and forces by more than two orders of magnitude, but is also moreaccurate than MLFFs based solely on Kohn-Sham DFT, while being more efficientand less sensitive to model parameters. We apply the framework to study thestructure of molten Al$_{0.88}$Si$_{0.12}$, the results suggesting noaggregation of Si atoms, in agreement with a previous Kohn-Sham study performedat an order of magnitude smaller length and time scales.

Kohn-Sham accuracy from orbital-free density functional theory via $\Delta$-machine learning