Predicting nuclear masses with the kernel ridge regression

Abstract

The kernel ridge regression (KRR) approach is employed to improve the nuclear mass predictions for the first time, and more importantly, a careful study of the expected predictive power in the neutron-rich region of the nuclear chart is presented, which is crucial for astrophysical simulations of nucleosynthesis processes. The ridge penalty influences the optimized kernel function significantly and plays an essential role in reducing the risk of overfitting and improving the accuracy of the predictions. By taking the WS4 mass model as an example, the mass for each nucleus in the nuclear chart is predicted with the KRR network, which is trained with the mass model residuals, i.e., deviations between experimental and calculated masses, of other nuclei with known masses. The resultant root-mean-square mass deviation from the available experimental data for the 2353 nuclei with $Z\ensuremath{\ge}8$ and $N\ensuremath{\ge}8$ can be reduced to 199 keV. This is at the same level with other machine-learning-rooted approaches, such as the radial basis function and Bayesian neural network approaches. However, with the Gaussian kernel, the present KRR approach provides strikingly different extrapolated masses for nuclei with unknown masses, since it automatically identifies the limit of the extrapolation distance. Therefore, it avoids the risk of worsening the mass description for nuclei at large extrapolation distances.