论文标题
无轨道DFT的数据驱动的动能密度拟合：线性与高斯过程回归
Data-driven kinetic energy density fitting for orbital-free DFT: linear vs Gaussian process regression
论文作者
论文摘要
我们研究了动能密度（KED）对密度依赖性变量的依赖性，这些变量已在先前关于无轨道DFT的动力学函数（KEF）（of-dft）的研究中提出。我们专注于数据分布以及数据和回归器选择的作用。我们比较了KED的未加权和加权线性和高斯过程回归，用于光金属和半导体。我们发现，与以前的文献中建议的密度依赖性变量相比，可能会导致良好的能量量依赖性的良好质量线性回归。这是通过基于KED直方图加权拟合来实现的。通过高斯工艺回归，获得了极好的KED拟合质量，超过了线性回归的质量，并且获得了良好的能量量依赖性，这比最佳线性回归的质量要好得多。我们发现，尽管将有效电位用作描述符可以改善线性KED拟合，但它并不能通过线性回归来提高能量依赖性的质量，但是通过高斯过程回归，它可以显着改善它。高斯过程回归也能够很好地表现，而无需数据加权。
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.
