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

TL;DR

R$^2$-PINN addresses persistent gradient vanishing and sampling bottlenecks in physics-informed neural networks applied to neutron diffusion equations by integrating a convolutional residual backbone (S-CNN) with an adaptive residual resampling (RAR) strategy. The approach enables accurate steady-state and transient predictions, and efficient eigenvalue searches for $k_{eff}$, demonstrated across 1D and 2D single- and multi-group diffusion problems including the 2D-IAEA benchmark. Key contributions include improved gradient propagation, adaptive sampling that concentrates points in high-residual regions, and substantial accuracy gains over FCN-based PINNs, with fast parameter search capabilities. The results indicate strong potential for real-time reactor-core analysis and multi-physics extensions in nuclear engineering.

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.

Figures (25)

• Figure 1: Infinite Plate Reactor.
• Figure 2: Material Distributionliu2.
• Figure 3: Geometric layout of the 2D-IAEA benchmark problemNone.
• Figure 4: Gradient Norm of Each Layer.
• Figure 5: PDE Points Distribution.