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<p>The neutron diffusion equation plays a pivotal role in nuclear reactor analysis. Nevertheless, employing the physics-informed neural network (PINN) method for its solution entails certain limitations. Conventional PINN approaches generally utilize a fully connected network (FCN) architecture that is susceptible to overfitting, training instability, and gradient vanishing as the network depth increases. These challenges result in accuracy bottlenecks in the solution. In response to these issues, the residual-based resample physics-informed neural network (R<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(^2\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mn>2</mn> </mmultiscripts> </math></EquationSource> </InlineEquation>-PINN) is proposed. It is an improved PINN architecture that replaces the FCN with a convolutional neural network with a shortcut (S-CNN). It incorporates skip connections to facilitate gradient propagation between network layers. Additionally, the incorporation of the residual adaptive resampling (RAR) mechanism dynamically increases the number of sampling points. This, in turn, enhances the spatial representation capabilities and overall predictive accuracy of the model. The experimental results illustrate that our approach significantly improves the convergence capability of the model and achieves high-precision predictions of the physical fields. Compared with conventional FCN-based PINN methods, R<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(^2\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mn>2</mn> </mmultiscripts> </math></EquationSource> </InlineEquation>-PINN effectively overcomes the limitations inherent in current methods. Thus, it provides more accurate and robust solutions for neutron diffusion equations.</p>

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Residual resampling-based physics-informed neural network for neutron diffusion equations

  • 期刊论文

  • 发表日期：

    2026年1月4日

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  • Heng Zhang,
  • Yun-Ling He,
  • Dong Liu,
  • Qin Hang,
  • He-Min Yao,
  • Di Xiang

摘要

The neutron diffusion equation plays a pivotal role in nuclear reactor analysis. Nevertheless, employing the physics-informed neural network (PINN) method for its solution entails certain limitations. Conventional PINN approaches generally utilize a fully connected network (FCN) architecture that is susceptible to overfitting, training instability, and gradient vanishing as the network depth increases. These challenges result in accuracy bottlenecks in the solution. In response to these issues, the residual-based resample physics-informed neural network (R \(^2\) 2 -PINN) is proposed. It is an improved PINN architecture that replaces the FCN with a convolutional neural network with a shortcut (S-CNN). It incorporates skip connections to facilitate gradient propagation between network layers. Additionally, the incorporation of the residual adaptive resampling (RAR) mechanism dynamically increases the number of sampling points. This, in turn, enhances the spatial representation capabilities and overall predictive accuracy of the model. The experimental results illustrate that our approach significantly improves the convergence capability of the model and achieves high-precision predictions of the physical fields. Compared with conventional FCN-based PINN methods, R \(^2\) 2 -PINN effectively overcomes the limitations inherent in current methods. Thus, it provides more accurate and robust solutions for neutron diffusion equations.