Abstract
In this paper, the artificial neural networks (ANN) based deep learning (DL) techniques were developed to solve the neutron diffusion problems for the continuous neutron flux distribution without domain discretization in advance. Due to its mesh-free property, the DL solution can easily be extended to complicated geometries. Two specific realizations of DL methods with different boundary treatments are developed and compared for accuracy and efficiency, including the boundary independent method (BIM) and boundary dependent method (BDM). The performance comparison on analytic benchmark indicates BDM being the preferred DL method. Novel constructions of trial function are proposed to generalize the application of BDM. For a more in-depth understanding of the BDM on diffusion problems, the influence of important hyper-parameters is further investigated. Numerical results indicate that the accuracy of BDM can reach hundreds of times higher than that of BIM on diffusion problems. This work can provide a new perspective for applying the DL method to nuclear reactor calculations.
Highlights
Neutron diffusion equation, as a simplified form with the P1 approximation of neutron transport equation [1,2], is commonly used in reactor core calculations for nuclear reactor design and analysis
Some numerical problems based on the neutron diffusion equation are employed to examine the computational performance of the boundary dependent method (BDM) and boundary independent method (BIM)
This paper introduces two mesh-free physicsinformed deep learning (PIDL) method, including the boundary dependent method (BDM)
Summary
As a simplified form with the P1 approximation of neutron transport equation [1,2], is commonly used in reactor core calculations for nuclear reactor design and analysis. Focusing on solving neutron diffusion equation, many mesh-based numerical methods have been proposed and employed by various groups. The pros and cons of these mesh-based methods are generally recognized and the accuracy of these methods is essentially limited by the number of nodes and the geometric shape of the problem under investigated [7]. These mesh-based methods can only obtain discrete solutions associated with the discretized nodes. A mesh independent and easy implemented computational method is more desired for problems with complex geometries
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