  Nuclear masses are predicted with the Bayesian neural networks by learning
the mass surface of even-even nuclei and the correlation energies to their
neighbouring nuclei. By keeping the known physics in various sophisticated mass
models and performing the delicate design of neural networks, the proposed
Bayesian machine learning (BML) mass model achieves an accuracy of $84$~keV,
which crosses the accuracy threshold of the $100$~keV in the experimentally
known region. It is also demonstrated the corresponding uncertainties of mass
predictions are properly evaluated, while the uncertainties increase by about
$50$~keV each step along the isotopic chains towards the unknown region. The
shell structures in the known region are well described and several important
features in the unknown region are predicted, such as the new magic numbers
around $N = 40$, the robustness of $N = 82$ shell, the quenching of $N = 126$
shell, and the smooth separation energies around $N = 104$.
