Combined Garvey Kelson Relations for Mass Determinations and Machine Learning

TL;DR

This paper develops optimized Garvey Kelson mass relations tailored for specific nuclear mass prediction tasks, demonstrating high accuracy and potential for integration into machine learning models for nuclear physics.

Contribution

It introduces three optimized Garvey Kelson relations for different prediction tasks, improving nuclear mass estimation accuracy and exploring their integration with machine learning.

Findings

Central mass prediction with 129 keV deviation

Corner mass prediction with 472 keV deviation

Overall measure with 35 keV deviation

Abstract

Simple Garvey Kelson mass relations applied in two regions are often used as an evaluation metric for machine learning based mass models. These relations have also been used in the training of some machine learning based models. Unfortunately, these Garvey Kelson relations do not broadly sum to zero as is sometimes assumed. In this manuscript, we generate three Garvey Kelson based mass relations that have been optimized with the goal of predicting nuclear masses the most accurately. These three relations have each been optimized for specific tasks. One relation has been optimized to predict the masses on the corner of a 5-by-5 grid. One has been optimized to predict the central mass on that grid, and the last has been optimized to work over the entire grid. Using these relations with the AME 2020 N & Z > 7 data, the central nucleus can be determined with a 129 keV standard deviation, any of the four corner masses with a 472 keV standard deviation, and the overall measure finds a 35 keV standard deviation for a per difference metric. We have compared these results with those from theoretical mass models and have tested the prediction and extrapolation capabilities of the relation that predicts corner masses. We also discuss how these relations can be implemented in machine learning based approaches.