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Machine learning the nuclear mass

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A Correction to this article was published on 05 November 2021

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Abstract

Background:

The masses of \(\sim\)2500 nuclei have been measured experimentally; however, >7000 isotopes are predicted to exist in the nuclear landscape from H (\(Z=1\)) to Og (\(Z=118\)) based on various theoretical calculations. Exploring the mass of the remaining isotopes is a popular topic in nuclear physics. Machine learning has served as a powerful tool for learning complex representations of big data in many fields.

Purpose:

We use Light Gradient Boosting Machine (LightGBM), which is a highly efficient machine learning algorithm, to predict the masses of unknown nuclei and to explore the nuclear landscape on the neutron-rich side from learning the measured nuclear masses.

Methods:

Several characteristic quantities (e.g., mass number and proton number) are fed into the LightGBM algorithm to mimic the patterns of the residual \(\delta (Z,A)\) between the experimental binding energy and the theoretical one given by the liquid-drop model (LDM), Duflo–Zucker (DZ, also dubbed DZ28) mass model, finite-range droplet model (FRDM, also dubbed FRDM2012), as well as the Weizsäcker–Skyrme (WS4) model to refine these mass models.

Results:

By using the experimental data of 80\(\%\) of known nuclei as the training dataset, the root mean square deviations (RMSDs) between the predicted and the experimental binding energy of the remaining 20% are approximately \(0.234\pm 0.022\), \(0.213\pm 0.018\), \(0.170\pm 0.011\), and \(0.222\pm 0.016\) MeV for the LightGBM-refined LDM, DZ model, WS4 model, and FRDM, respectively. These values are approximately 90%, 65%, 40%, and 60% smaller than those of the corresponding origin mass models. The RMSD for 66 newly measured nuclei that appeared in AME2020 was also significantly improved. The one-neutron and two-neutron separation energies predicted by these refined models are consistent with several theoretical predictions based on various physical models. In addition, the two-neutron separation energies of several newly measured nuclei (e.g., some isotopes of Ca, Ti, Pm, and Sm) predicted with LightGBM-refined mass models are also in good agreement with the latest experimental data.

Conclusions:

LightGBM can be used to refine theoretical nuclear mass models and predict the binding energy of unknown nuclei. Moreover, the correlation between the input characteristic quantities and the output can be interpreted by SHapley additive exPlanations (a popular explainable artificial intelligence tool), which may provide new insights for developing theoretical nuclear mass models.

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Acknowledgements

Fruitful discussions with Prof. Jie Meng, Prof. Hong-Fei Zhang, Prof. Yu-Min Zhao, and Dr. Na-Na Ma are greatly appreciated. The authors acknowledge support by computing server C3S2 at the Huzhou University. The mass table for the LightGBM-refined mass models is available in the Supplemental Material.

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Authors and Affiliations

  1. College of Physics Science and Technology, Shenyang Normal University, Shenyang, 110034, China

    Ze-Peng Gao & Ling Liu

  2. School of Science, Huzhou University, Huzhou, 313000, China

    Ze-Peng Gao, Yong-Jia Wang, Qing-Feng Li & Cai-Wan Shen

  3. HiSilicon Research Department, Huawei Technologies Co., Ltd., Shenzhen, 518000, China

    Hong-Liang Lü

  4. Institute of Modern Physics, Chinese Academy of Science, Lanzhou, 730000, China

    Qing-Feng Li

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  1. Ze-Peng Gao
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Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Ze-Peng Gao, Yong-Jia Wang, Hong-Liang Lü, Qing-Feng Li, Cai-Wan Shen and Ling Liu. The first draft of the manuscript was written by Ze-Peng Gao, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript. The contributions of Hong-Liang Lü are non-Huawei achievements.

Corresponding authors

Correspondence to Yong-Jia Wang or Qing-Feng Li.

Additional information

This work was supported in part by the National Science Foundation of China (Nos. U2032145, 11875125, 12047568, 11790323, 11790325, and 12075085), the National Key Research and Development Program of China (No. 2020YFE0202002), and the “Ten Thousand Talent Program” of Zhejiang Province (No. 2018R52017).

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Gao, ZP., Wang, YJ., Lü, HL. et al. Machine learning the nuclear mass. NUCL SCI TECH 32, 109 (2021). https://doi.org/10.1007/s41365-021-00956-1

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