  The neutron diffusion equation plays a pivotal role in the analysis of
nuclear reactors. Nevertheless, employing the Physics-Informed Neural Network
(PINN) method for its solution entails certain limitations. Traditional PINN
approaches often utilize fully connected network (FCN) architecture, which is
susceptible to overfitting, training instability, and gradient vanishing issues
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(R2-PINN) is proposed, which proposes an
improved PINN architecture that replaces the FCN with a Convolutional Neural
Network with a shortcut(S-CNN), incorporating skip connections to facilitate
gradient propagation between network layers. Additionally, the incorporation of
the Residual Adaptive Resampling (RAR) mechanism dynamically increases sampling
points, enhancing the spatial representation capabilities and overall
predictive accuracy of the model. The experimental results illustrate that our
approach significantly improves the model's convergence capability, achieving
high-precision predictions of physical fields. In comparison to traditional
FCN-based PINN methods, R2-PINN effectively overcomes the limitations inherent
in current methods, providing more accurate and robust solutions for neutron
diffusion equations.
