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Solving Multi-Group Neutron Diffusion Eigenvalue Problem with Decoupling Residual Loss Function
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DOI：10.4208/cicp.OA-2024-0176.png)
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Abstract
En 中文
In the midst of the neural network's success in solving partial differential equations, tackling eigenvalue problems using neural networks remains a challenging task. However, the Physics Constrained-General Inverse Power Method Neural Network (PC-GIPMNN) approach was proposed and successfully applied to solve the single-group critical problems in reactor physics. This paper aims to solve critical problems in multi-group scenarios and in more complex geometries. Hence, inspired by the merits of traditional source iterative method, which can overcome the ill-condition of the right side of the equations effectively and solve the multi-group problem effectively, we propose two residual loss function called Decoupling Residual loss function and Direct Iterative loss function. Our loss function can deal with multi-group eigenvalue problem, and also single-group eigenvalue problem. Using the new residual loss functions, our study solves one-dimensional, two-dimensional, and three-dimensional multi-group problems in nuclear reactor physics without prior data. In numerical experiments, our approach demonstrates superior generalization capabilities compared to previous work.
Keywords:
Deep learning
eigenvalue problem
nuclear reactors
multi-group problem.
Journal
IF:
3.1
Papers:
75
Citations:
4.3K