Kinetic energy (KE) functional is crucial to speed up density functional theory calculation. However, deriving it accurately through traditional physics reasoning is challenging. We develop a generally applicable KE functional estimator for a one-dimensional (1D) extended system using a machine learning method. Our end-to-end solution combines the dimensionality reduction method with the Gaussian process regression, and simple scaling method to adapt to various 1D lattices. In addition to reaching chemical accuracy in KE calculation, our estimator also performs well on KE functional derivative prediction. Integrating this machine learning KE functional into the current orbital free density functional theory scheme is able to provide us with expected ground state electron density.

动能（KE）泛函对于加速密度泛函理论计算至关重要。然而，通过传统的物理推理准确地推导出它是具有挑战性的。我们使用机器学习方法为一维 (1D) 扩展系统开发了一个普遍适用的 KE 函数估计器。我们的端到端解决方案结合了降维方法与高斯过程回归，以及简单的缩放方法以适应各种一维格。除了在 KE 计算中达到化学精度外，我们的估计器在 KE 泛函导数预测方面也表现良好。将这种机器学习 KE 泛函集成到当前的轨道自由密度泛函理论方案中，能够为我们提供预期的基态电子密度。