Machine Learning-Assisted Hartree–Fock Approach for Energy Level Calculations in the Neutral Ytterbium Atom

Data-driven machine learning approaches with precise predictive capabilities are proposed to address the long-standing challenges in the calculation of complex many-electron atomic systems, including high computational costs and limited accuracy. In this work, we develop a general workflow for machine learning-assisted atomic structure calculations based on the Cowan code's Hartree-Fock with relativistic corrections (HFR) theory. The workflow incorporates enhanced ElasticNet and XGBoost algorithms, refined using entropy weight methodology to optimize performance. This semi-empirical framework is applied to calculate and analyze the excited state energy levels of the 4<i>f</i> closed-shell Yb I atom, providing insights into the applicability of different algorithms under various conditions. The reliability and advantages of this innovative approach are demonstrated through comprehensive comparisons with ab initio calculations, experimental data, and other theoretical results.