Principal Components of Nuclear Mass Model Residuals

TL;DR

The paper addresses the challenge of missing physics in nuclear mass predictions by applying Principal Component Analysis to the residuals of six widely used mass models. By constructing residual vectors over thousands of nuclei and performing PCA, it reveals that no single principal component universally dominates model discrepancies; residuals are largely uncorrelated and exhibit model-specific structures. Some PCs align with known physics such as shell and deformation effects, while others correspond to fine, hard-to-interpret features, underscoring the need for targeted, model-by-model improvements. This work provides a data-driven framework to identify and interpret deficiencies in nuclear mass models, guiding more nuanced refinements rather than universal corrections.

Abstract

Principal Component Analysis (PCA) is applied to the residuals of six widely used nuclear mass models to uncover systematic deviations and identify missing physical effects in theoretical nuclear mass predictions. By analyzing the principal components of nuclear mass model residuals, this study reveals that no single dominant pattern governs the discrepancies across models. Instead, the residual structures are largely uncorrelated, indicating that current nuclear mass models fail to capture underlying nuclear residual effects in distinct and model-specific ways. These findings suggest that improvements to nuclear mass models should be guided by model-specific residual analyses rather than a one-size-fits-all approach.

Figures (3)

• Figure 1: Variance contribution rates (blue bars) and cumulative contribution rates (red line) of principal components for nuclear mass model residuals. The variance contribution rate is an important concept in the principal components analysis, which represents the contribution rate of each principal component in the representation of the models.
• Figure 2: Principal components, i.e., PC1 (a), PC2 (b), ..., and PC6 (f) of nuclear mass models with the values scaled to the range between -1 and 1. The boundary of nuclei with known masses in AME2020 is shown by the black contour lines.Dotted lines indicate the magic numbers.
• Figure 3: Radar plot with radii given by squared weights of the principal components for the residuals of a specific nuclear mass model, i.e., the $|a_i|^2$ in $M_{\rm res}^{\rm Model}=\sum_i a_i \cdot {\rm PC}i$. The weight for PC1 in each plot is scaled to 1, with all other principal components undergoing corresponding scaling.