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Machine learning of kinetic energy functionals (KEF), in particular kineticenergy density (KED) functionals, has recently attracted attention as apromising way to construct KEFs for orbital-free density functional theory(OF-DFT). Neural networks (NN) and kernel methods including Gaussian processregression (GPR) have been used to learn Kohn-Sham (KS) KED from density-baseddescriptors derived from KS DFT calculations. The descriptors are typicallyexpressed as functions of different powers and derivatives of the electrondensity. This can generate large and extremely unevenly distributed datasets,which complicates effective application of machine learning techniques. Veryuneven data distributions require many training data points, can causeoverfitting, and ultimately lower the quality of a ML KED model. We show thatone can produce more accurate ML models from fewer data by working withpartially averaged density-dependent variables and KED. Averaging palliates theissue of very uneven data distributions and associated difficulties ofsampling, while retaining enough spatial structure necessary for working withinthe paradigm of KEDF. We use GPR as a function of partially spatially averagedterms of the 4th order gradient expansion and the Kohn-Sham effective potentialand obtain accurate and stable (with respect to different random choices oftraining points) kinetic energy models for Al, Mg, and Si simultaneously fromas few as 2000 samples (about 0.3% of the total KS DFT data). In particular,accuracies on the order of 1% in a measure of the quality of energy-volumedependence B' = \frac{E(V_0-\Delta V)-2E(V_0)+E(V_0 + \DeltaV)}{\big(\frac{\Delta V}{V_0}\big)^2} are obtained simultaneously for all threematerials.

Machine learning of kinetic energy densities with target and feature averaging: better results with fewer training data