Abstract The accuracy of the Finite-Range Droplet Model 2012 (FRDM) in describing the $\alpha$ decay energies of the 947 known heavy and superheavy nuclei is studied. It is clearly found that there are obvious discrepancies between the $\alpha$ decay energies obtained by FRDM and those reported by the evaluated atomic mass table AME 2020 (AME), in particular that FRDM underestimates the experimental $\alpha$ decay energies of the superheavy nuclei. The $\alpha$ decay energies of known nuclei obtained by FRDM are optimized, i.e. FRDM-NN, using a neural network approach and the accuracy is significantly improved. The $\alpha$ decay energy systematics obtained by both FRDM and FRDM-NN show the obvious shell effect at neutron number $N=184$, implying that the $N=184$ may be the magic number of the superheavy nucleus region. The $\alpha$ decay half-lives of known superheavy nuclei are calculated using the Generalized Liquid Drop Model (GLDM) and the Royer formula with the input of the optimized $\alpha$ decay energies obtained by FRDM-NN, and the calculations can reproduce the experimental data well. The $\alpha$ decay half-lives of unknown superheavy nuclei, in particular superheavy nuclei with $Z=119$ and 120, are predicted by using the GLDM and the Royer formula with the input of the $\alpha$ decay energy obtained by FRDM-NN. The relative error of two types of predicted $\alpha$ decay half-lives and superposition are analysed, and the average predictions are given. The $\alpha$ decay energies predicted by FRDM-NN and the $\alpha$ decay half-lives calculated by the GLDM and the Royer formula can provide a reference for the experimental synthesis of new superheavy elements with $Z=119$ and 120.
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