Average energy data of <b>β<sup>–</sup></b> decay nuclei based on neural networks

WEI Kaiwen; SHANG Tianshuai; TIAN Ronghe; YANG Dong; LI Chunjuan; CHEN Jun; LI Jian; HUANG Xiaolong; ZHU Jiali

doi:10.7498/aps.74.20250655

Abstract

The average β energy data and average γ energy data of the β^–-decay nuclei play an important role in many fields of nuclear technology and scientific research, such as the decay heat and antineutrino spectrum calculation for different kinds of reactors. However, the reliable experimental measurements of the average energies for many nuclei are lacking, and the theoretical calculation needs to be improved to meet the requirements for accuracy in the technical applications.In this study, the average β, γ and neutrino energies of the β^–-decay nuclei are investigated by the neural network method based on the newly evaluated experimental data of 543 nuclei that are selected from a total of 1136 β^–-decay nuclei. In the neural network approach, three different feature sets are used for model training. Each feature set contains a feature characteristic value (one of the $T_{1/2}$, $\left( {1}/{T_{1/2}} \right)^{1/5}$, and$Q/3$), along with five identical feature values (Z, N, parity of Z, parity of N, and $\Delta Z$).The three feature values are selected based on the physical mechanism below. 1) The average energy is obviously related to Q value and approximately taken as $Q/3$ in the reactor industry. Therefore, the $Q/3$ is chosen as one feature value. 2) The half-live is related to the Q value of β^–-decay, and $T_{1/2}$ is considered. 3) According to the Sargent’s law, $\left( {1}/{T_{1/2}} \right)^{1/5} \propto Q$, a more accurate $\left( {1}/{T_{1/2}} \right)^{1/5}$ value is selected.As a result, for the feature set of $T_{1/2}$, the training results for all three types of average energies are unsatisfactory. For the other groups, the relative errors of the average β energy data, are 19.32% and 28.11% for $\left( {1}/{T_{1/2}} \right)^{1/5}$ and $Q/3$ feature groups in the training set, and 82% and 56.9% in the validation set; the relative errors of the average γ energy are 28.9% and 76.9% for $\left( {1}/{T_{1/2}} \right)^{1/5}$ and $Q/3$ feature sets, respectively, and they are both >100% in the validation set; for the average neutrino energy, the relative errors in the training set are 27.82% and 35.33% for $\left( {1}/{T_{1/2}} \right)^{1/5}$ and $Q/3$ feature group, and 76.32% and 37.76% in the validation set, respectively.Considering the accuracy comparison of the three groups, the $Q/3$ feature set is chosen to predict the average energy data of nuclei in the fission product region (mass numbers range from 66 to 172), which lacks reliable experimental data. As a result, the average energy data with predicted values for 291 nuclei are supplemented. Besides, a comparison is made between the calculated data and the evaluated experimental data through the nuclide chart. It is found that the neural network accurately predicts the experimental data for the average β and neutrino energies which exhibit relatively strong regularity. However, it shows significant deviations in predictions for average gamma energy (relative error in the training set is 76.9%). Large deviation also emerges in the odd-odd nuclei and nuclei near magic numbers. This study confirms that integrating empirical relationships and physical principles can effectively improve the performance of the neural network, and simultaneously reveals the relationship between data regularity and model generalization capability. These findings provide a basis for using physical mechanisms to optimize machine learning models in the future.

Keywords:

Authors and contacts

1.
Key Laboratory of Measurement and Calibration Technology for National Defense Science and Technology, China Institute of Atomic Energy, Beijing 102413, China
2.
College of Physics, Jilin University, Changchun 130012, China
3.
China Nuclear Data Center, China Institute of Atomic Energy of China, Beijing 102413, China
4.
National Basic Science Data Center, Beijing 100190, China

Corresponding author: TIAN Ronghe, viccocautoo603@gmail.com

Funds: Project supported by the Foundation of the National Basic Science Data Center (Grant No. NBSDCDB-23) and the Foundation of the Key Laboratory of Nuclear Data foundation (Grant No. JCKY2023201C151).

FullText HTML

References

[1]	Algora A, Tain J, Rubio B, Fallot M, Gelletly W 2021 Eur. Phys. J. A 57 85 Google Scholar
[2]	Nichols A 2015 J. Nucl. Sci. Technol. 52 17 Google Scholar
[3]	Rana M A 2008 Nucl. Sci. Tech. 19 117 Google Scholar
[4]	Song Q F, Zhu L, Guo H, Su J 2023 Nucl. Sci. Tech. 34 32 Google Scholar
[5]	Xiao K, Li P C, Wang Y J, Liu F H, Li Q F 2023 Nucl. Sci. Tech. 34 62 Google Scholar
[6]	Greenwood R, Helmer R, Putnam M, Watts K 1997 Nucl. Instrum. Methods Phys. Res. A 390 95 Google Scholar
[7]	Valencia E, Tain J, Algora A, et al. 2017 Phys. Rev. C 95 024320 Google Scholar
[8]	Tengblad O, Aleklett K, Von Dincklage R, Lund E, Nyman G, Rudstam G 1989 Nucl. Phys. A 503 136 Google Scholar
[9]	Nichols A, Dimitriou P, Algora A, et al. 2023 Eur. Phys. J. A 59 78 Google Scholar
[10]	Yoshida T, Nakasima R 1981 J. Nucl. Sci. Technol. 18 393 Google Scholar
[11]	Fang J, Zhang X, Shi M, Niu Z 2025 Eur. Phys. J. A 61 1 Google Scholar
[12]	Fang J, Chen J, Niu Z 2022 Phys. Rev. C 106 054318 Google Scholar
[13]	Azevedo M, Ferreira R, Dimarco A, Barbero C A, Samana A R, Possidonio D 2020 Brazil. J. Phys. 50 57 Google Scholar
[14]	Nakata H, Tachibana T, Yamada M 1995 Nucl. Phys. A 594 27 Google Scholar
[15]	Nakata H, Tachibana T, Yamada M 1997 Nucl. Phys. A 625 521 Google Scholar
[16]	Tachibana T, Yamada M, Yoshida Y 1990 Prog. Theor. Phys. 84 641 Google Scholar
[17]	Borzov I 2006 Nucl. Phys. A 777 645 Google Scholar
[18]	Kumar V, Srivastava P C 2023 Eur. Phys. J. A 59 237 Google Scholar
[19]	Ni D, Ren Z 2012 J. Phys. G 39 125105 Google Scholar
[20]	Nabi J U, Ishfaq M 2020 New Astron. 78 101356 Google Scholar
[21]	Engel J, Bender M, Dobaczewski J, Nazarewicz W, Surman R 1999 Phys. Rev. C 60 014302 Google Scholar
[22]	Minato F, Bai C 2013 Phys. Rev. Lett. 110 122501 Google Scholar
[23]	Moller P, Nix J, Myers W, Swiatecki W 1995 At. Data Nucl. Data Tables 59 185 Google Scholar
[24]	Möller P, Randrup J 1990 Nucl. Phys. A 514 1 Google Scholar
[25]	Audi G, Bersillon O, Blachot J, Wapstra A 2003 Nucl. Phys. A 729 3 Google Scholar
[26]	Moller P, Nix J, Kratz K 1997 At. Data Nucl. Data Tables 66 131 Google Scholar
[27]	Möller P, Pfeiffer B, Kratz K L 2003 Phys. Rev. C 67 055802 Google Scholar
[28]	Soloviev V G 2020 Theory of Atomic Nuclei, Quasi-particle and Phonons. (Boca Raton, FL: CRC Press) p226
[29]	Kuz-Min V, Soloviev V 1988 Nucl. Phys. A 486 118 Google Scholar
[30]	Soloviev V, Sushkov A 1989 Phys. Lett. B 216 259 Google Scholar
[31]	Luo D, Clark B K 2019 Phys. Rev. Lett. 122 226401 Google Scholar
[32]	Yoshida S 2020 Phys. Rev. C 102 024305 Google Scholar
[33]	Chen Y, Wu X 2024 Int. J. Mod. Phys. E 33 2450012 Google Scholar
[34]	Hizawa N, Hagino K, Yoshida K 2023 Phys. Rev. C 108 034311 Google Scholar
[35]	Wu X, Ren Z, Zhao P 2022 Phys. Rev. C 105 L031303 Google Scholar
[36]	Yang Z X, Fan X H, Li Z P, Liang H 2023 Phys. Lett. B 840 137870 Google Scholar
[37]	Utama R, Chen W C, Piekarewicz J 2016 J. Phys. G 43 114002 Google Scholar
[38]	Wu D, Bai C, Sagawa H, Zhang H 2020 Phys. Rev. C 102 054323 Google Scholar
[39]	Xian Z Y, Ya Y, An R 2025 Phys. Lett. B 868 139662 Google Scholar
[40]	Jiao B B 2024 Int. J. Mod. Phys. E 33 2450019 Google Scholar
[41]	Zhang X, He H, Qu G, Liu X, Zheng H, Lin W, Han J, Ren P, Wada R 2024 Phys. Rev. C 110 014316 Google Scholar
[42]	Zhang X, Liu X, Zheng H, et al. 2025 IEEE Trans. Nucl. Sci. 72 795 Google Scholar
[43]	Rodríguez U B, Vargas C Z, Gonçalves M, Duarte S B, Guzmán F 2019 J. Phys. G 46 115109 Google Scholar
[44]	Freitas P S, Clark J W 2019 arXiv: 1910.12345 [nucl-th]
[45]	Ma N N, Bao X J, Zhang H F 2021 Chin. Phys. C 45 024105 Google Scholar
[46]	Yuan Z, Bai D, Ren Z, Wang Z 2022 Chin. Phys. C 46 024101 Google Scholar
[47]	Li W, Zhang X, Niu Y, Niu Z 2023 J. Phys. G 51 015103 Google Scholar
[48]	Luo J, Xu Y, Li X, Wang J, Zhang Y, Deng J, Zhang F, Ma N 2025 Phys. Rev. C 111 034330 Google Scholar
[49]	Akkoyun S 2020 Nucl. Instrum. Methods Phys. Res. B 462 51 Google Scholar
[50]	Ma C W, Peng D, Wei H L, Niu Z M, Wang Y T, Wada R 2020 Chin. Phys. C 44 014104 Google Scholar
[51]	Sun Q K, Zhang Y, Hao Z R, et al. 2025 Nucl. Sci. Tech. 36 52 Google Scholar
[52]	Li W, Liu L, Niu Z, Niu Y, Huang X 2024 Phys. Rev. C 109 044616 Google Scholar
[53]	Özdoğan H, Üncü Y A, Şekerci M, Kaplan A 2024 Appl. Radiat. Isot. 204 111115 Google Scholar
[54]	Lay D, Flynn E, Giuliani S A, Nazarewicz W, Neufcourt L 2024 Phys. Rev. C 109 044305 Google Scholar
[55]	郭粤颖, 唐湘琪, 刘辉鑫, 吴鑫辉 2025 核技术 48 050003 Google Scholar Guo Y Y, Tang X Q, Liu H X, Wu X H 2025 Nucl. Tech. 48 050003 Google Scholar
[56]	Utama R, Piekarewicz J 2017 Phys. Rev. C 96 044308 Google Scholar
[57]	Neufcourt L, Cao Y, Nazarewicz W, Viens F 2018 Phys. Rev. C 98 034318 Google Scholar
[58]	Utama R, Piekarewicz J 2018 Phys. Rev. C 97 014306 Google Scholar
[59]	Neufcourt L, Cao Y, Nazarewicz W, Olsen E, Viens F 2019 Phys. Rev. Lett. 122 062502 Google Scholar
[60]	Neufcourt L, Cao Y, Giuliani S, Nazarewicz W, Olsen E, Tarasov O B 2020 Phys. Rev. C 101 014319 Google Scholar
[61]	Lu Y, Shang T, Du P, Li J, Liang H, Niu Z 2025 Phys. Rev. C 111 014325 Google Scholar
[62]	Zeng L X, Yin Y Y, Dong X X, Geng L S 2024 Phys. Rev. C 109 034318 Google Scholar
[63]	Yiu T C, Liang H, Lee J 2024 Chin. Phys. C 48 024102 Google Scholar
[64]	Yüksel E, Soydaner D, Bahtiyar H 2024 Phys. Rev. C 109 064322 Google Scholar
[65]	谭凯中, 高琬晴, 刘健 2025 核技术 48 050010 Google Scholar Tan K Z, Gao W Q, Liu J 2025 Nucl. Tech. 48 050010 Google Scholar
[66]	ENSDF: Evaluated Nuclear Structure Data File, National Nuclear Data Center https://www.nndc.bnl.gov/ensdf/ [2025-07-07]
[67]	Wang M, Huang W J, Kondev F G, Audi G, Naimi S 2021 Chin. Phys. C 45 030003 Google Scholar
[68]	Sargent B 1933 Proc. R. Soc. London, Ser. A 139 659 Google Scholar

Cited By

图 1 实验(543)与神经网络(834)所得β粒子平均能量系统变化的核素图

Figure 1. Systematic variation of average β energy values from experiment (543) and neural network (834) in the nuclear chart.

DownLoad: Full-Size Img PowerPoint

图 2 实验(543)与神经网络(834)所得γ射线平均能量系统变化的核素图

Figure 2. Systematic variation of average γ energy values from experiment (543) and neural network (834) in the nuclear chart.

DownLoad: Full-Size Img PowerPoint

图 3 实验(543)与神经网络(834)所得中微子平均能量系统变化的核素图

Figure 3. Systematic variation of average neutrino energy values from experiment (543) and neural network (834) in the nuclear chart.

DownLoad: Full-Size Img PowerPoint

表 1 神经网络的超参数集

Table 1. Hyper parameters of neural network

层数	名称	神经元数目	激活函数
0	输入层	6
1	隐藏层	60	Tanh
2	隐藏层	60	Tanh
3	隐藏层	60	Tanh
4	隐藏层	60	Tanh
5	隐藏层	60	Tanh
6	输出层	1

DownLoad: CSV

表 2 其他超参数

Table 2. Other hyper parameters

其他超参数	值和特征
批大小	16
损失函数	均方差
优化器	RMSprop
学习速率	$ 1\times10^{-5} $

DownLoad: CSV

表 3 平均能量计算结果

Table 3. Calculation results of average energies

平均能量类型	误差类型	特征组1	特征组2	特征组3
β粒子平均能	训练误差	$> 100{\text{%}} $	19.32%	28.11%
β粒子平均能	验证误差	$> 100{\text{%}} $	82%	56.9%
γ射线平均能	训练误差	$> 100{\text{%}} $	28.9%	76.9%
γ射线平均能	验证误差	$> 100{\text{%}} $	$> 100{\text{%}} $	$> 100{\text{%}} $
中微子平均能	训练误差	$> 100{\text{%}} $	27.82%	35.33%
中微子平均能	验证误差	$> 100{\text{%}} $	76.32%	37.76%

DownLoad: CSV

[1]	Algora A, Tain J, Rubio B, Fallot M, Gelletly W 2021 Eur. Phys. J. A 57 85 Google Scholar
[2]	Nichols A 2015 J. Nucl. Sci. Technol. 52 17 Google Scholar
[3]	Rana M A 2008 Nucl. Sci. Tech. 19 117 Google Scholar
[4]	Song Q F, Zhu L, Guo H, Su J 2023 Nucl. Sci. Tech. 34 32 Google Scholar
[5]	Xiao K, Li P C, Wang Y J, Liu F H, Li Q F 2023 Nucl. Sci. Tech. 34 62 Google Scholar
[6]	Greenwood R, Helmer R, Putnam M, Watts K 1997 Nucl. Instrum. Methods Phys. Res. A 390 95 Google Scholar
[7]	Valencia E, Tain J, Algora A, et al. 2017 Phys. Rev. C 95 024320 Google Scholar
[8]	Tengblad O, Aleklett K, Von Dincklage R, Lund E, Nyman G, Rudstam G 1989 Nucl. Phys. A 503 136 Google Scholar
[9]	Nichols A, Dimitriou P, Algora A, et al. 2023 Eur. Phys. J. A 59 78 Google Scholar
[10]	Yoshida T, Nakasima R 1981 J. Nucl. Sci. Technol. 18 393 Google Scholar
[11]	Fang J, Zhang X, Shi M, Niu Z 2025 Eur. Phys. J. A 61 1 Google Scholar
[12]	Fang J, Chen J, Niu Z 2022 Phys. Rev. C 106 054318 Google Scholar
[13]	Azevedo M, Ferreira R, Dimarco A, Barbero C A, Samana A R, Possidonio D 2020 Brazil. J. Phys. 50 57 Google Scholar
[14]	Nakata H, Tachibana T, Yamada M 1995 Nucl. Phys. A 594 27 Google Scholar
[15]	Nakata H, Tachibana T, Yamada M 1997 Nucl. Phys. A 625 521 Google Scholar
[16]	Tachibana T, Yamada M, Yoshida Y 1990 Prog. Theor. Phys. 84 641 Google Scholar
[17]	Borzov I 2006 Nucl. Phys. A 777 645 Google Scholar
[18]	Kumar V, Srivastava P C 2023 Eur. Phys. J. A 59 237 Google Scholar
[19]	Ni D, Ren Z 2012 J. Phys. G 39 125105 Google Scholar
[20]	Nabi J U, Ishfaq M 2020 New Astron. 78 101356 Google Scholar
[21]	Engel J, Bender M, Dobaczewski J, Nazarewicz W, Surman R 1999 Phys. Rev. C 60 014302 Google Scholar
[22]	Minato F, Bai C 2013 Phys. Rev. Lett. 110 122501 Google Scholar
[23]	Moller P, Nix J, Myers W, Swiatecki W 1995 At. Data Nucl. Data Tables 59 185 Google Scholar
[24]	Möller P, Randrup J 1990 Nucl. Phys. A 514 1 Google Scholar
[25]	Audi G, Bersillon O, Blachot J, Wapstra A 2003 Nucl. Phys. A 729 3 Google Scholar
[26]	Moller P, Nix J, Kratz K 1997 At. Data Nucl. Data Tables 66 131 Google Scholar
[27]	Möller P, Pfeiffer B, Kratz K L 2003 Phys. Rev. C 67 055802 Google Scholar
[28]	Soloviev V G 2020 Theory of Atomic Nuclei, Quasi-particle and Phonons. (Boca Raton, FL: CRC Press) p226
[29]	Kuz-Min V, Soloviev V 1988 Nucl. Phys. A 486 118 Google Scholar
[30]	Soloviev V, Sushkov A 1989 Phys. Lett. B 216 259 Google Scholar
[31]	Luo D, Clark B K 2019 Phys. Rev. Lett. 122 226401 Google Scholar
[32]	Yoshida S 2020 Phys. Rev. C 102 024305 Google Scholar
[33]	Chen Y, Wu X 2024 Int. J. Mod. Phys. E 33 2450012 Google Scholar
[34]	Hizawa N, Hagino K, Yoshida K 2023 Phys. Rev. C 108 034311 Google Scholar
[35]	Wu X, Ren Z, Zhao P 2022 Phys. Rev. C 105 L031303 Google Scholar
[36]	Yang Z X, Fan X H, Li Z P, Liang H 2023 Phys. Lett. B 840 137870 Google Scholar
[37]	Utama R, Chen W C, Piekarewicz J 2016 J. Phys. G 43 114002 Google Scholar
[38]	Wu D, Bai C, Sagawa H, Zhang H 2020 Phys. Rev. C 102 054323 Google Scholar
[39]	Xian Z Y, Ya Y, An R 2025 Phys. Lett. B 868 139662 Google Scholar
[40]	Jiao B B 2024 Int. J. Mod. Phys. E 33 2450019 Google Scholar
[41]	Zhang X, He H, Qu G, Liu X, Zheng H, Lin W, Han J, Ren P, Wada R 2024 Phys. Rev. C 110 014316 Google Scholar
[42]	Zhang X, Liu X, Zheng H, et al. 2025 IEEE Trans. Nucl. Sci. 72 795 Google Scholar
[43]	Rodríguez U B, Vargas C Z, Gonçalves M, Duarte S B, Guzmán F 2019 J. Phys. G 46 115109 Google Scholar
[44]	Freitas P S, Clark J W 2019 arXiv: 1910.12345 [nucl-th]
[45]	Ma N N, Bao X J, Zhang H F 2021 Chin. Phys. C 45 024105 Google Scholar
[46]	Yuan Z, Bai D, Ren Z, Wang Z 2022 Chin. Phys. C 46 024101 Google Scholar
[47]	Li W, Zhang X, Niu Y, Niu Z 2023 J. Phys. G 51 015103 Google Scholar
[48]	Luo J, Xu Y, Li X, Wang J, Zhang Y, Deng J, Zhang F, Ma N 2025 Phys. Rev. C 111 034330 Google Scholar
[49]	Akkoyun S 2020 Nucl. Instrum. Methods Phys. Res. B 462 51 Google Scholar
[50]	Ma C W, Peng D, Wei H L, Niu Z M, Wang Y T, Wada R 2020 Chin. Phys. C 44 014104 Google Scholar
[51]	Sun Q K, Zhang Y, Hao Z R, et al. 2025 Nucl. Sci. Tech. 36 52 Google Scholar
[52]	Li W, Liu L, Niu Z, Niu Y, Huang X 2024 Phys. Rev. C 109 044616 Google Scholar
[53]	Özdoğan H, Üncü Y A, Şekerci M, Kaplan A 2024 Appl. Radiat. Isot. 204 111115 Google Scholar
[54]	Lay D, Flynn E, Giuliani S A, Nazarewicz W, Neufcourt L 2024 Phys. Rev. C 109 044305 Google Scholar
[55]	郭粤颖, 唐湘琪, 刘辉鑫, 吴鑫辉 2025 核技术 48 050003 Google Scholar Guo Y Y, Tang X Q, Liu H X, Wu X H 2025 Nucl. Tech. 48 050003 Google Scholar
[56]	Utama R, Piekarewicz J 2017 Phys. Rev. C 96 044308 Google Scholar
[57]	Neufcourt L, Cao Y, Nazarewicz W, Viens F 2018 Phys. Rev. C 98 034318 Google Scholar
[58]	Utama R, Piekarewicz J 2018 Phys. Rev. C 97 014306 Google Scholar
[59]	Neufcourt L, Cao Y, Nazarewicz W, Olsen E, Viens F 2019 Phys. Rev. Lett. 122 062502 Google Scholar
[60]	Neufcourt L, Cao Y, Giuliani S, Nazarewicz W, Olsen E, Tarasov O B 2020 Phys. Rev. C 101 014319 Google Scholar
[61]	Lu Y, Shang T, Du P, Li J, Liang H, Niu Z 2025 Phys. Rev. C 111 014325 Google Scholar
[62]	Zeng L X, Yin Y Y, Dong X X, Geng L S 2024 Phys. Rev. C 109 034318 Google Scholar
[63]	Yiu T C, Liang H, Lee J 2024 Chin. Phys. C 48 024102 Google Scholar
[64]	Yüksel E, Soydaner D, Bahtiyar H 2024 Phys. Rev. C 109 064322 Google Scholar
[65]	谭凯中, 高琬晴, 刘健 2025 核技术 48 050010 Google Scholar Tan K Z, Gao W Q, Liu J 2025 Nucl. Tech. 48 050010 Google Scholar
[66]	ENSDF: Evaluated Nuclear Structure Data File, National Nuclear Data Center https://www.nndc.bnl.gov/ensdf/ [2025-07-07]
[67]	Wang M, Huang W J, Kondev F G, Audi G, Naimi S 2021 Chin. Phys. C 45 030003 Google Scholar
[68]	Sargent B 1933 Proc. R. Soc. London, Ser. A 139 659 Google Scholar

[1]	WANG Peng, MAIMAITINIYAZI Maimaitiabudula. Quantum dynamics of machine learning. Acta Physica Sinica, 2025, 74(6): 060701. doi: 10.7498/aps.74.20240999
[2]	LIU Yujie, WANG Zhenyu, LEI Hang, ZHANG Guoyu, XIAN Jiawei, GAO Zhibin, SUN Jun, SONG Haifeng, DING Xiangdong. Machine learning-driven elasticity prediction in advanced inorganic materials via convolutional neural networks. Acta Physica Sinica, 2025, 74(12): 120702. doi: 10.7498/aps.74.20250127
[3]	ZHANG Suncheng, HAN Tongwei, WANG Rumeng, YANG Yantao, ZHANG Xiaoyan. Prediction and optimization of negative Poisson’s ratio in rhombic perforated graphene based on machine learning. Acta Physica Sinica, 2025, 74(9): 096201. doi: 10.7498/aps.74.20241624
[4]	LIU Zhaosheng, ZHANG Qiao, NING Yongqi, FU Xiujiao, ZOU Daifeng, WANG Junnian, ZHAO Yuqing. Prediction of High Curie Temperature Janus Materials Based on Machine Learning and First-Principles Calculations. Acta Physica Sinica, 2025, 74(22): . doi: 10.7498/aps.74.20251026
[5]	CHEN Haijun, SHENG Haowen, HUANG Wenhao, WU Binqi, ZHAO Tianliang, BAO Xiaojun. Research on stability and decay properties of superheavy nuclei based on neural network method. Acta Physica Sinica, 2025, 74(19): 192301. doi: 10.7498/aps.74.20250720
[6]	WU Yanghai, DU Hailong, XUE Lei, LI Jiaxian, XUE Miao, ZHENG Guoyao. Machine learning-based prediction of heat load on Tokamak divertor target plates. Acta Physica Sinica, 2025, 74(13): 135205. doi: 10.7498/aps.74.20250381
[7]	Zhang Jia-Hui. Machine learning for in silico protein research. Acta Physica Sinica, 2024, 73(6): 069301. doi: 10.7498/aps.73.20231618
[8]	Ouyang Xin-Jian, Zhang Yan-Xing, Wang Zhi-Long, Zhang Feng, Chen Wei-Jia, Zhuang Yuan, Jie Xiao, Liu Lai-Jun, Wang Da-Wei. Modeling ferroelectric phase transitions with graph convolutional neural networks. Acta Physica Sinica, 2024, 73(8): 086301. doi: 10.7498/aps.73.20240156
[9]	Ma Rui-Yao, Wang Xin, Li Shu, Yong Heng, Shangguan Dan-Hua. An efficient calculation method for particle transport problems based on neural network. Acta Physica Sinica, 2024, 73(7): 072802. doi: 10.7498/aps.73.20231661
[10]	Guo Wei-Chen, Ai Bao-Quan, He Liang. Reveal flocking phase transition of self-propelled active particles by machine learning regression uncertainty. Acta Physica Sinica, 2023, 72(20): 200701. doi: 10.7498/aps.72.20230896
[11]	Liu Ye, Niu He-Ran, Li Bing-Bing, Ma Xin-Hua, Cui Shu-Wang. Application of machine learning in cosmic ray particle identification. Acta Physica Sinica, 2023, 72(14): 140202. doi: 10.7498/aps.72.20230334
[12]	Li Wei, Long Lian-Chun, Liu Jing-Yi, Yang Yang. Classification of magnetic ground states and prediction of magnetic moments of inorganic magnetic materials based on machine learning. Acta Physica Sinica, 2022, 71(6): 060202. doi: 10.7498/aps.71.20211625
[13]	Chen Jiang-Zhi, Yang Chen-Wen, Ren Jie. Machine learning based on wave and diffusion physical systems. Acta Physica Sinica, 2021, 70(14): 144204. doi: 10.7498/aps.70.20210879
[14]	Zhang Yao, Zhang Yun-Bo, Chen Li. Deep-learning-assisted micro impurity detection on an optical surface. Acta Physica Sinica, 2021, 70(16): 168702. doi: 10.7498/aps.70.20210403
[15]	Wang Wei, Jie Quan-Lin. Identifying phase transition point of J₁-J₂ antiferromagnetic Heisenberg spin chain by machine learning. Acta Physica Sinica, 2021, 70(23): 230701. doi: 10.7498/aps.70.20210711
[16]	Wang Peng-Ju, Fan Jun-Yu, Su Yan, Zhao Ji-Jun. Energetic potential of hexogen constructed by machine learning. Acta Physica Sinica, 2020, 69(23): 238702. doi: 10.7498/aps.69.20200690
[17]	Zhang Xian, Wang Hong-Li. Selective forgetting extreme learning machine and its application to time series prediction. Acta Physica Sinica, 2011, 60(8): 080504. doi: 10.7498/aps.60.080504
[18]	Wang Yong-Sheng, Sun Jin, Wang Chang-Jin, Fan Hong-Da. Prediction of the chaotic time series from parameter-varying systems using artificial neural networks. Acta Physica Sinica, 2008, 57(10): 6120-6131. doi: 10.7498/aps.57.6120
[19]	Peng Jian-Hua, Yu Hong-Jie. Associative memory and segmentation in the neural system under stimulation of stochastic or chaotic perceptual singals. Acta Physica Sinica, 2007, 56(8): 4353-4360. doi: 10.7498/aps.56.4353
[20]	CHEN SHU, CHANG SHENG-JIANG, YUAN JING-HE, ZHANG YAN-XIN, K.W.WONG. ADAPTIVE TRAINING AND PRUNING FOR NEURAL NETWORKS:ALGORITHMS AND APPLICATION. Acta Physica Sinica, 2001, 50(4): 674-681. doi: 10.7498/aps.50.674

Catalog

Vol. 74, Issue 18 - 2025-09-20

Metrics

Abstract views: 1128
PDF Downloads: 9
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板

Average energy data of β^– decay nuclei based on neural networks

Abstract

Authors and contacts

Corresponding author: TIAN Ronghe, viccocautoo603@gmail.com

FullText HTML

References

Cited By

Catalog

Metrics

Authors

Referees

About Journal

About

Search

Article

留言板

Average energy data of β– decay nuclei based on neural networks

Abstract

Authors and contacts

Corresponding author: TIAN Ronghe, viccocautoo603@gmail.com

FullText HTML

References

Cited By

Catalog

Metrics

Publishing process

Authors

Referees

About Journal

About

Average energy data of β^– decay nuclei based on neural networks