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

摘要: The neutron diffusion equation plays a pivotal role in the analysis of nuclear reactors. Nevertheless, employ#2;
ing 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 ac#2;
curacy 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 gra#2;
dient 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 com#2;
parison 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.