Refining mass formulas for astrophysical applications: A Bayesian neural network approach

Background: Exotic nuclei, particularly those near the drip lines, are at the core of one of the fundamental questions driving nuclear structure and astrophysics today: What are the limits of nuclear binding? Exotic nuclei play a critical role in both informing theoretical models as well as in our understanding of the origin of the heavy elements. Purpose: Our aim is to refine existing mass models through the training of an artificial neural network that will mitigate the large model discrepancies far away from stability. Methods: The basic paradigm of our two-pronged approach is an existing mass model that captures as much as possible of the underlying physics followed by the implementation of a Bayesian neural network (BNN) refinement to account for the missing physics. Bayesian inference is employed to determine the parameters of the neural network so that model predictions may be accompanied by theoretical uncertainties. Results: Despite the undeniable quality of the mass models adopted in this work, we observe a significant improvement (of about 40%) after the BNN refinement is implemented. Indeed, in the specific case of the Duflo-Zuker mass formula, we find that the rms deviation relative to experiment is reduced from sigma(rms) = 0.503 MeV to sigma(rms) = 0.286 MeV. These newly refined mass tables are used to map the neutron drip lines (or rather drip bands) and to study a few critical r-process nuclei. Conclusions: The BNN approach is highly successful in refining the predictions of existing mass models. In particular, the large discrepancy displayed by the original bare models in regions where experimental data are unavailable is considerably quenched after the BNN refinement. This lends credence to our approach and has motivated us to publish refined mass tables that we trust will be helpful for future astrophysical applications.