Physically Interpretable Machine Learning for nuclear masses

Abstract

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 ${\sigma }_{\text{RMS}}\sim 186$ keV match to data for the training set and ${\sigma }_{\text{RMS}}\sim 316$ keV for the entire AME with $Z\ge 20$. We show that our general methodology can be interpreted using feature importance.

5 pages, 3 figures, comments welcome

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• Nuclear mass predictions based on Bayesian neural network approach with pairing and shell effects
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• Machine-learning approach to finite-size effects in systems with strongly interacting fermions

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