Simple deep-learning approach for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>α</mml:mi></mml:math>-decay half-life studies
Nana Ma, Tian Liang Zhao, Wenxia Wang, Hongfei Zhang
Abstract
To exploit the potential of deep learning (DL) in $\ensuremath{\alpha}$-decay studies, we refocus on the essence of DL, which is a nonlinear input-output mapping with a hierarchical learning process. Here, instead of using the residual between experimental data and the calculation, the idea of training DL directly by experimental $\ensuremath{\alpha}$-decay half-life is used. The Levenberg-Marquardt backpropagation algorithm is utilized for fixing free parameters of the mapping. A $\mathcal{K}$-fold cross-validation method is introduced to avoid overfitting and improve the generalization performance of DL, as well as to determine hyperparameters effectively. We find that DL results with both three-dimensional ${Z,A,{Q}_{\ensuremath{\alpha}}}$ and four-dimensional ${Z,A,{Q}_{\ensuremath{\alpha}},l}$ input vectors achieve an impressive accuracy that matches or even exceeds the traditional models. Especially, DL realizes an efficient extraction of the pertinent shell and odd-even staggering effects of half-life solely from the characteristics of ${Q}_{\ensuremath{\alpha}}$ values. On the other hand, the universal decay law (UDL) describes the classical relationship between ${Z,A,{Q}_{\ensuremath{\alpha}}}$ and a-decay half-life, which is homologous with DL. Heuristically, we add the contributions of the angular momentum and blocking effect of unpaired nucleons in the UDL and develop an improved UDL formula.