Statistical learnability of nuclear masses
This work addresses the long-standing problem in nuclear physics of accurately modeling nuclear masses, but it is incremental as it applies existing statistical learning methods to this domain.
The paper tackles the challenge of predicting atomic nuclear masses with high precision, which has large deviations from experiments, by applying statistical learning theory to bound prediction errors and validating these bounds with neural network calculations, showing that current models operate near the knowledge limit defined by learning theory.
After more than 80 years from the seminal work of Weizsäcker and the liquid drop model of the atomic nucleus, deviations from experiments of mass models ($\sim$ MeV) are orders of magnitude larger than experimental errors ($\lesssim$ keV). Predicting the mass of atomic nuclei with precision is extremely challenging. This is due to the non--trivial many--body interplay of protons and neutrons in nuclei, and the complex nature of the nuclear strong force. Statistical theory of learning will be used to provide bounds to the prediction errors of model trained with a finite data set. These bounds are validated with neural network calculations, and compared with state of the art mass models. Therefore, it will be argued that the nuclear structure models investigating ground state properties explore a system on the limit of the knowledgeable, as defined by the statistical theory of learning.