Exact Conditions for the Machine-learned Kinetic Energy in Density Functional Theory

Orbital-free density functional theory (OF-DFT) is an appealing approach to obtain the ground state density and energy of electronic systems. However, its usefulness is limited by the unknown non-interacting kinetic energy functional. Some Machine Learning studies have suggested a trade-off between data and use of physical constraints for accurate results. Here, we study the effects of exact conditions in the process of ML model construction within the simplest possible setting: a Fully-connected Neural Network (FNN) that includes semi-local information. Training on the hydrogen molecule at various separations and imposing the stationarity condition of DFT leads to Mean Absolute Errors of ∼10 mHa. In contrast, typical values of ∼200 mHa were observed in the absence of this stationarity constraint. Further improvement is expected after hyperparameter tuning. A similar behavior is anticipated and will be studied for more complex systems.