The Deep Learning Method to Search Effective Multiplication Factor of Nuclear Reactor Directly

Liu Dong; Tang Lei; An Ping; Zhang Bin; Jiang Yong

doi:10.13832/j.jnpe.2023.05.0006

Volume 44 Issue 5

Oct. 2023

Turn off MathJax

Article Contents

Article Navigation > Nuclear Power Engineering > 2023 > 44(5): 6-14

Liu Dong, Tang Lei, An Ping, Zhang Bin, Jiang Yong. The Deep Learning Method to Search Effective Multiplication Factor of Nuclear Reactor Directly[J]. Nuclear Power Engineering, 2023, 44(5): 6-14. doi: 10.13832/j.jnpe.2023.05.0006

Citation:

Liu Dong, Tang Lei, An Ping, Zhang Bin, Jiang Yong. The Deep Learning Method to Search Effective Multiplication Factor of Nuclear Reactor Directly[J]. Nuclear Power Engineering, 2023, 44(5): 6-14. doi: 10.13832/j.jnpe.2023.05.0006

Citation:

PDF( 20133 KB)

The Deep Learning Method to Search Effective Multiplication Factor of Nuclear Reactor Directly

doi: 10.13832/j.jnpe.2023.05.0006

Liu Dong^{1, 2
,},
Tang Lei^{1, 2},
An Ping^{1, 2},
Zhang Bin^{1, 2},
Jiang Yong¹

1.
Science and Technology on Reactor System Design Technology Laboratory, Nuclear Power Institute of China, Chengdu, 610213, China
2.
CNNC Engineering Research Center of Nuclear Energy Software and Digital Reactor, Chengdu, 610213, China

Received Date: 2022-10-11
Accepted Date: 2022-11-27
Rev Recd Date: 2022-11-27
Publish Date: 2023-10-13

Abstract

Abstract

It's a basic problem in the reactor criticality calculation to determine the effective multiplication factor k_eff. At present, the source iteration method is widely used in the industry. Based on the theory of artificial intelligence deep learning method to solve differential equations, this paper puts forward a new method, which takes k_eff and the weights of neural network neurons as machine learning optimization parameters, calculates the weighted loss function formed by substituting neural network functions into neutron differential equations, and simultaneously approaches neutron fluence rate and searches for k_eff directly. The mathematical form of eigenvalue of neutron differential equation, the setting method of initial neural network, the weighting factor of loss function, convergence criterion and other important factors affecting deep learning performance and the corresponding performance improvement schemes are discussed. The correctness of the method and the effectiveness of the learning performance improvement schemes are verified by numerical calculation of various examples. The results have explored a new technical way to calculate the k_eff of nuclear reactors, which is an important scientific problem in neutron physics.

FullText(HTML)

References(16)

References

[1]	谢仲生, 曹良志, 张少泓. 核反应堆物理分析[M]. 第五版. 西安: 西安交通大学出版社, 2020: 69-90.
[2]	谢仲生, 邓力. 中子输运理论数值计算方法[M]. 西安: 西北工业大学出版社, 2005: 11-50.
[3]	XIE Y C, WANG Y H, MA Y, et al. Neural network based deep learning method for multi-dimensional neutron diffusion problems with novel treatment to boundary[J]. Journal of Nuclear Engineering, 2021, 2(4): 533-552. doi: 10.3390/jne2040036
[4]	RAISSI M, PERDIKARIS P, KARNIADAKIS G E. Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations[J]. Journal of Computational Physics, 2019, 378: 686-707. doi: 10.1016/j.jcp.2018.10.045
[5]	刘东,罗琦,唐雷,等. 基于PINN深度机器学习技术求解多维中子学扩散方程[J]. 核动力工程,2022, 43(2): 1-8. doi: 10.13832/j.jnpe.2022.02.0001
[6]	GALIB S M, BHOWMIK P K, AVACHAT A V, et al. A comparative study of machine learning methods for automated identification of radioisotopes using NaI gamma-ray spectra[J]. Nuclear Engineering and Technology, 2021, 53(12): 4072-4079. doi: 10.1016/j.net.2021.06.020
[7]	周蜀林. 偏微分方程[M]. 北京: 北京大学出版社, 2005: 1-16.
[8]	HAGAN M T, DEMUTH H B, BEALE M H, et al. Neural network design[M]. 2nd ed. Oklahoma: Martin Hagan, 2014: (2-1)-(2-25).
[9]	BYRD R H, GILBERT J C, NOCEDAL J. A trust region method based on interior point techniques for nonlinear programming[J]. Mathematical Programming, 2000, 89(1): 149-185. doi: 10.1007/PL00011391
[10]	DUMOUCHEL W H, O'BRIEN F L. Integrating a robust option into a multiple regression computing environment[C]//Computer Science and Statistics: Proceedings of the 21st Symposium on the Interface. Alexandria, VA: American Statistical Association, 1989: 41-48.
[11]	KINGMA D P, BA J. Adam: a method for stochastic optimization[C]//Proceedings of the 3rd International Conference on Learning Representations. San Diego, 2014: 1-15.
[12]	杨强, 张宇, 戴文渊, 等. 迁移学习[M]. 北京: 机械工业出版社, 2020: 2-79.
[13]	AN P, MA Y Q, XIAO P, et al. Development and validation of reactor nuclear design code CORCA-3D[J]. Nuclear Engineering and Technology, 2019, 51(7): 1721-1728. doi: 10.1016/j.net.2019.05.015
[14]	DOWNAR T, XU Y, SEKER V. PARCS v3.0 US NRC core neutronics simulator theory manual[M]. Rockville, MD: US NRC, 2012: 5-98.
[15]	卢皓亮,吴宏春,曹良志,等. 中子输运方程的三角形节块S_N方法研究[J]. 核动力工程,2006, 27(5): 6-11. doi: 10.3969/j.issn.0258-0926.2006.05.002
[16]	杜书华. 输运问题的计算机模拟[M]. 长沙: 湖南科学技术出版社, 1988: 130-150, 304-345.