Solving Multi-Dimensional Neutron Diffusion Equation Using Deep Machine Learning Technology Based on PINN Model

Liu Dong; Luo Qi; Tang Lei; An Ping; Yang Fan

doi:10.13832/j.jnpe.2022.02.0001

Volume 43 Issue 2

Apr. 2022

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Liu Dong, Luo Qi, Tang Lei, An Ping, Yang Fan. Solving Multi-Dimensional Neutron Diffusion Equation Using Deep Machine Learning Technology Based on PINN Model[J]. Nuclear Power Engineering, 2022, 43(2): 1-8. doi: 10.13832/j.jnpe.2022.02.0001

Citation:

Liu Dong, Luo Qi, Tang Lei, An Ping, Yang Fan. Solving Multi-Dimensional Neutron Diffusion Equation Using Deep Machine Learning Technology Based on PINN Model[J]. Nuclear Power Engineering, 2022, 43(2): 1-8. doi: 10.13832/j.jnpe.2022.02.0001

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Solving Multi-Dimensional Neutron Diffusion Equation Using Deep Machine Learning Technology Based on PINN Model

doi: 10.13832/j.jnpe.2022.02.0001

Liu Dong^{1, 2, 3
,},
Luo Qi³,
Tang Lei^{1, 2},
An Ping^{1, 2},
Yang Fan¹

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
3.
Committee on Science and Technology of China National Nuclear Corporation, Beijing, 100822, China

Received Date: 2021-12-07
Accepted Date: 2022-02-14
Rev Recd Date: 2022-01-26
Publish Date: 2022-04-02

Abstract

Abstract

This paper elaborates the physics-informed neural network model (PINN), constructs a deep neural network as a trial function, substitutes it into the neutron diffusion equation to form a residual, and takes it as the weighted loss function of machine learning, and then approaches the numerical solution of the neutron diffusion equation by deep machine learning technique; According to the characteristics of diffusion equation, this paper puts forward innovative key technologies such as accelerated convergence method of eigenvalue equation, efficient parallel search technology of effective multiplication coefficient (k_eff), learning sample grid point uneven distribution strategy, and analyzes the sensitivity of key parameters such as neural network depth, neuron number, boundary condition loss function weight and so on. The verification calculation results show that the method has good accuracy, and the proposed key technology has remarkable results, and explores a new technical approach for the numerical solution of the neutron diffusion equation.

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References(15)

References

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