Data-driven kinetic energy density fitting for orbital-free DFT: linear vs Gaussian process regression

TL;DR

This paper compares linear and Gaussian process regression methods for fitting kinetic energy densities in orbital-free DFT, demonstrating that Gaussian processes outperform linear models in fit quality and energy-volume dependence, especially with effective potential descriptors.

Contribution

It introduces a comprehensive comparison of linear and Gaussian process regressions for KED fitting, highlighting the advantages of Gaussian processes and the impact of data weighting and descriptors.

Findings

Gaussian process regression yields superior KED fit quality.

Weighted fitting improves linear regression energy-volume dependence.

Effective potential descriptors enhance Gaussian process regression performance.

Abstract

We study the dependence of kinetic energy densities (KED) on density-dependent variables that have been suggested in previous works on kinetic energy functionals (KEF) for orbital-free DFT (OF-DFT). We focus on the role of data distribution and on data and regressor selection. We compare unweighted and weighted linear and Gaussian process regressions of KED for light metals and a semiconductor. We find that good quality linear regression resulting in good energy-volume dependence is possible over density-dependent variables suggested in previous literature. This is achieved with weighted fitting based on KED histogram. With Gaussian process regressions, excellent KED fit quality well exceeding that of linear regressions is obtained as well as a good energy-volume dependence which was somewhat better than that of best linear regressions. We find that while the use of the effective potential as a descriptor improves linear KED fitting, it does not improve the quality of the energy-volume dependence with linear regressions but substantially improves it with Gaussian process regression. Gaussian process regression is also able to perform well without data weighting.