Ability of the radial basis function approach to extrapolate nuclear mass

Abstract

The ability of the radial basis function (RBF) approach to extrapolate the masses of nuclei in neutron-rich and superheavy regions is investigated in combination with the Duflo-Zuker (DZ31), Hartree–Fock-Bogoliubov (HFB27), finite-range droplet model (FRDM12) and Weizsäcker-Skyrme (WS4) mass models. It is found that when the RBF approach is employed with a simple linear basis function, different mass models have different performances in extrapolating nuclear masses in the same region, and a single mass model may have different performances when it is used to extrapolate nuclear masses in different regions. The WS4 and FRDM12 models (two macroscopic–microscopic mass models), combined with the RBF approach, may perform better when extrapolating the nuclear mass in the neutron-rich and superheavy regions.

Machine learning in nuclear physics at low and intermediate energies

“…Moreover, the importance of input fea-tures in refining mass models was analyzed by investigating the correlation between the input characteristic quantities and the output, which may provide new insights for further developing nuclear mass models [45]. In addition, the RBF approach [46] and its improved version of RBF with odd-even effects (RBFoe) [47] have also been widely used to improve the predictions of nuclear masses [48][49][50][51][52][53][54]. By including a regularizer to reduce the risk of overfitting of RBF approach, the KRR [55], the KRR with odd-even effects [56,57], and the gradient KRR (a multi-task learning framework) [58] have been developed to improve the predictions of nuclear masses.…”

Studies of different kernel functions in nuclear mass predictions with kernel ridge regression

“…For nuclear physics, ML applications can be traced back to early 1990s [26,27], and recently, it has been widely adopted to nuclear masses [28][29][30][31][32][33][34][35][36][37][38][39][40][41], charge radii [36,[42][43][44][45], decays and reactions [46][47][48][49][50][51][52][53], ground and excited states [54][55][56][57][58], nuclear landscape [59,60], fission yields [61-63], nuclear liquid-gas phase transition [64], variational calculations [65,66], nuclear energy density functional [67], etc. In nuclear mass studies, ML approaches, such as the radial basis function (RBF) approach [28,29,[68][69][70][71], the Bayesian neural network (BNN) approach [31][32][33]72], and the kernel ridge regression (KRR) appro...…”