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

TL;DR

This paper introduces R2-PINN, a novel neural network architecture combining CNNs with skip connections and adaptive resampling to improve the accuracy and stability of solving neutron diffusion equations.

Contribution

The paper proposes R2-PINN, an improved PINN architecture using CNNs with skip connections and adaptive resampling to address overfitting and training issues in traditional PINNs.

Findings

R2-PINN achieves higher accuracy than traditional PINNs.

The method demonstrates improved convergence and robustness.

Experimental results confirm enhanced predictive performance.

Abstract

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.