Physically Interpretable Machine Learning for nuclear masses

We present a novel approach to modeling the ground state mass of atomic nuclei based directly on a probabilistic neural network constrained by relevant physics. Our Physically Interpretable Machine Learning (PIML) approach incorporates knowledge of physics by using a physically motivated feature space in addition to a soft physics constraint that is implemented as a penalty to the loss function. We train our PIML model on a random set of \(\sim\)20\% of the Atomic Mass Evaluation (AME) and predict the remaining \(\sim\)80\%. The success of our methodology is exhibited by the unprecedented \(\sigma_\textrm{RMS}\sim186\) keV match to data for the training set and \(\sigma_\textrm{RMS}\sim316\) keV for the entire AME with \(Z \geq 20\). We show that our general methodology can be interpreted using feature importance.