This paper introduces a new way to correct errors in theoretical nuclear mass models using an interpretable machine learning method called a Kolmogorov–Arnold Network (KAN). The authors build a hybrid called KAN-WS4 that learns the small, complicated differences between model predictions and experimental masses. For the WS4 model, the hybrid reduces the root-mean-square error from about 0.3 MeV to 0.16 MeV on the data used in the study.

The team focused on the residuals — the differences between theory and experiment — rather than trying to replace existing physics models. They trained the KAN to predict that residual term using a dataset of 2,340 nuclei taken from the Atomic Mass Evaluation 2020 (AME2020). Only nuclei with proton number Z and neutron number N both at least 8 and with experimental uncertainties below 100 keV were included. The goal was to improve accuracy where the theoretical models miss small, high-frequency patterns.

KANs are based on the Kolmogorov–Arnold representation theorem, which says a multivariable function can be written as sums of one-dimensional functions. Practically, a KAN uses learnable nonlinear transformations on each input edge and then sums them. That contrasts with common multilayer perceptrons (MLPs) that stack many layers. The authors argue this structure is more data-efficient for small, complex datasets. They fed the network four physically motivated inputs: proton number Z, neutron number N, a pairing quantity P that encodes even/odd effects and scales with the mass number A = N + Z, and a shell-effect quantity S formed from distances to the nearest proton and neutron “magic numbers.” The proton magic numbers used were 8, 20, 28, 50, 82 and 126; the neutron list added 184.

Why this matters: nuclear masses are a key input for many physics topics, from nuclear structure to element formation in stars. Some applications, like the rapid neutron-capture process (r-process) in astrophysics, need mass predictions near 0.1 MeV accuracy. By cutting the residuals for an established model, the KAN approach moves predictions closer to that goal. The KAN also gives interpretable outputs. A feature-importance analysis in the paper flags the proton number as the most influential factor in the residuals. That suggests there may be systematic biases in how proton-related terms are handled in existing theoretical models. The authors tested the method with five different mass models to show it can be applied more widely.