Neutron noise calculation: A comparative study between SP3 theory and diffusion theory

Gong, Hang; Chen, Zhang; Wu, Wenbin; Peng, Xingjie; Li, Qing

doi:10.1016/j.anucene.2021.108184

Cited by 6 publications

(1 citation statement)

References 28 publications

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“…Although problems R2 and R3 denote that all the control rods are inserted, problem R2 resembles heavily inserted control rods, and problem R3 resembles slightly inserted control rods. To generate the necessary data to validate the accuracy of GIPMNN, PC-GIPMNN, and DRM, FreeFEM [67][68][69][70][71][72][73] is utilized to solve these problems in Table 1. FreeFEM is a partial differential equation solver for non-linear multi-physics systems using the finite element method.…”

Section: One-dimensional Slab Reactormentioning

confidence: 99%

Physics-constrained neural network for solving discontinuous interface K-eigenvalue problem with application to reactor physics

Yang,

Deng

et al. 2023

NUCL SCI TECH

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Machine learning-based modeling of reactor physics problems has attracted increasing interest in recent years. Despite some progress in one-dimensional problems, there is still a paucity of benchmark studies that are easy to solve using traditional numerical methods albeit still challenging using neural networks for a wide range of practical problems. We present two networks, namely the Generalized Inverse Power Method Neural Network (GIPMNN) and Physics-Constrained GIPMNN (PC-GIPIMNN) to solve K-eigenvalue problems in neutron diffusion theory. GIPMNN follows the main idea of the inverse power method and determines the lowest eigenvalue using an iterative method. The PC-GIPMNN additionally enforces conservative interface conditions for the neutron flux. Meanwhile, Deep Ritz Method (DRM) directly solves the smallest eigenvalue by minimizing the eigenvalue in Rayleigh quotient form. A comprehensive study was conducted using GIPMNN, PC-GIPMNN, and DRM to solve problems of complex spatial geometry with variant material domains from the field of nuclear reactor physics. The methods were compared with the standard finite element method. The applicability and accuracy of the methods are reported and indicate that PC-GIPMNN outperforms GIPMNN and DRM.

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