Combined Garvey Kelson Relations for Mass Determinations and Machine Learning
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.