Deep-Learning Paradigm Achieves Global Precision in Nuclear Charge Density Predictions
The charge density distribution of an atomic nucleus is a fundamental quantity for understanding nuclear structure physics. However, owing to experimental challenges and theoretical complexities, obtaining systematic, high-precision, and universally applicable predictions has long been a formidable task. A research team from Jilin University has now successfully predicted these distributions using a deep neural network (DNN) model, marking a significant leap in theoretical prediction accuracy.
Data-Driven Nuclear Structure Research
Traditional studies of nuclear charge density have primarily relied on theoretical frameworks such as density functional theory, which often suffer from limited predictive accuracy. This work pioneers a new data-driven, “physics-informed” paradigm. A DNN was trained by integrating experimental charge radius data from 1,014 nuclei. Compared to conventional methods, this model reduces the root-mean-square error in charge radius predictions by over 50%, signaling a decisive shift from purely theoretical calculations to a paradigm that effectively integrates experimental data.
Innovative Approach Marries Physical Mechanisms with Artificial Intelligence
The team proposed an innovative “physics-informed” training strategy featuring a two-stage optimization process. Initially, the DNN was trained to predict Fourier–Bessel coefficients based on Relativistic Continuum Hartree–Bogoliubov (RCHB) theory. It was subsequently fine-tuned using experimental charge radii. The model takes proton number, neutron number, distance to magic numbers, and a pairing parameter as inputs, and outputs 17 Fourier–Bessel coefficients that describe the charge density distribution, enabling a unified and precise description of both charge density and charge radius.
Experimental Data Validation and Significant Improvement in Predictive Performance
Tests on isotopes of nickel, palladium, mercury, and bismuth demonstrated that the DNN-predicted charge radii closely match experimental values, yielding a root-mean-square error of only 0.0149 fm—a substantial improvement over earlier DNN models and RCHB theory. Furthermore, the model exhibited superior capability in predicting central density and tail structures for nuclei such as chromium and zinc compared to traditional methods.
Broad Prospects for Multidisciplinary Applications
This research not only provides a high-precision dataset for nuclear structure theory but also opens new avenues for cross-disciplinary applications. Accurate nuclear charge-density distributions can advance multiple fields: they refine atomic spectral calculations, constrain parameters of the nuclear-matter equation of state, and supply critical inputs for nuclear-reaction networks in extreme astrophysical environments. Moreover, these results offer valuable benchmarks for tests of quantum electrodynamics, determinations of fundamental constants, and searches for physics beyond the Standard Model.
Ushering Nuclear Physics into a New Era of “ Intelligent Prediction ”
The research team plans to further refine the model architecture, extend its application to broader nuclear regions, and incorporate additional experimental data. This effort paves the way for advancing the understanding of nuclear structure and its roles in fundamental and applied sciences.
“By deeply integrating physical mechanisms with machine learning, we have not only improved the accuracy of nuclear charge density predictions but also provided a reliable data foundation for nuclear physics, atomic physics, and even fundamental physics research,” said Prof. Jian Li, the lead researcher. “This work demonstrates the immense potential of artificial intelligence in basic scientific inquiry, and we will continue to promote its application to a wider range of nuclear structure problems in the future.”
The complete study is via by DOI: https://doi.org/10.1007/s41365-026-01905-6
Nuclear Science and Techniques
Computational simulation/modeling
Not applicable
Predictions of charge density distributions for nuclei with Z ≥ 8
19-Mar-2026