Study of yrast and yrare low-lying excited states using machine learning approaches*

Abstract The low-lying excitation energies of the states in even-even nuclei are studied using two modern machine learning algorithms: the Light Gradient Boosting Machine (LightGBM) and Sparse Variational Gaussian Process (SVGP). The obtained results demonstrate that both LightGBM and SVGP perform well on the training and validation datasets when informed by a physics-based feature space. A detailed comparison of the results obtained for and states using the Hartree-Fock-Bogoliubov theory extended by the generator coordinate method and mapped onto a five-dimensional collective quadrupole Hamiltonian shows that both ML algorithms outperform this model in terms of accuracy. The extrapolation capabilities of these algorithms were further validated using newly measured 12 data points of and states, which were not included in the training set. In addition, the partial dependence plot method and the Shapley additive explanations method are used as interpretability tools to analyze the relationship between the input features and model predictions. These tools provide in-depth insights into how the input features influence the prediction of low-lying excitation energies and help identify the most important features that drive the prediction, which are valuable for understanding the low-lying excitation energies.