Deep learning model realizes global highly accurate nuclear charge density prediction covering a wide range of nuclei

Deep learning paradigm achieves world-class accuracy in nuclear charge density prediction
The charge density distribution of an atomic nucleus is a fundamental quantity for understanding nuclear structural physics. However, obtaining systematic, highly accurate, and universally applicable predictions has long been a challenge due to experimental challenges and theoretical complexity. A research team from Jilin University successfully predicted these distributions using a deep neural network (DNN) model, significantly improving the theoretical prediction accuracy.

Data-driven nuclear structure research
Previous studies of nuclear charge density have mainly relied on theoretical frameworks such as density functional theory, which often have limited predictive accuracy. This research pioneers a new data-driven “physics-based” paradigm. The DNN was trained by integrating experimental charge radius data from 1,014 nuclei. Compared to traditional methods, this model reduces the root-mean-square error in charge radius prediction by more than 50%, marking a decisive shift from purely theoretical calculations to a paradigm that effectively integrates experimental data.

Combining physical mechanisms and artificial intelligence with an innovative approach
The team proposed an innovative “physics-based” training strategy featuring a two-step optimization process. Initially, DNN was trained to predict Fourier-Bessel coefficients based on relativistic continuum Hartley-Bogoliubov (RCHB) theory. It was then fine-tuned using the experimental charge radius. The model takes as input the number of protons, the number of neutrons, the distance to the magic number, and the pairing parameters and outputs 17 Fourier Bessel coefficients that describe the charge density distribution, allowing a unified and accurate description of both charge density and charge radius.

experimental data Verification and significant improvement of predictive performance
Tests on nickel, palladium, mercury, and bismuth isotopes demonstrate that the DNN-predicted charge radius is in close agreement with experimental values, with a root-mean-square error of only 0.0149 fm. This is a significant improvement over previous DNN models and RCHB theory. Moreover, the model showed superior ability to predict the central density and tail structure of nuclei such as chromium and zinc compared to traditional methods.

Broad prospects for interdisciplinary applications
This study not only provides a high-precision dataset for nuclear structure theory but also opens new avenues for interdisciplinary applications. Accurate nuclear charge density distributions can advance multiple fields. It improves atomic spectral calculations, constrains the parameters of the equation of state of nuclear materials, and provides critical input to nuclear reaction networks in extreme astrophysical environments. Furthermore, these results provide a valuable benchmark for testing quantum electrodynamics, determining fundamental constants, and exploring physics beyond the Standard Model.

Leading nuclear physics into a new era “intelligent predictions”
The research team plans to further refine the model’s architecture, extend its application to a broader nuclear domain, and incorporate additional experimental data. This effort paves the way to advancing our understanding of nuclear structure and its role in basic and applied science.

“By deeply integrating physical mechanisms and machine learning, we have not only improved the accuracy of nuclear charge density prediction, but also provided a reliable data foundation for nuclear physics, atomic physics, and even fundamental physics research,” said principal investigator Professor Jian Li. “This work demonstrates the immense potential of artificial intelligence in fundamental scientific investigations and will continue to advance its application to a broader range of nuclear structure problems in the future.”

The complete study is provided by DOI: https://doi.org/10.1007/s41365-026-01905-6