Research on the high-performance computing method for the neutron diffusion spatiotemporal kinetics equation based on the convolutional neural network

Abstract

Due to the uncertainty of computational results and the lack of interpretability of models in solving physical field equations in current deep learning, this paper designs a convolutional neural network that can be used to solve the neutron diffusion spatiotemporal kinetics equation in polar and cylindrical coordinate systems. This algorithm directly utilizes the macroscopic cross-section of the material without using the lattice homogenization method, replaces the finite volume method with the extended matrices, and solves the extended matrices using the convolutional kernels instead of the iterative algorithms. Taking the simplified Tsinghua High Flux Reactor (THFR) as an example, the feasibility of the algorithm is verified on the PyTorch platform and compared with the calculation results of the source iteration method running on the GPU. The calculation results show that when the number of grids in the radial and axial sections of the simplified THFR model is 804,600 and 3,576,000, respectively, and the algorithm is iterated 3000 times, the normalized power of the convolutional neural network and the source iteration method converges to 10⁻¹⁰, and the maximum point by point error of the neutron flux density of the above two algorithms converges to 10⁻⁵. The computational time consumed by the convolutional neural network is approximately 880.64 s and 3729.62 s, which reduces the computational time by 4.66% and 5.05% compared to the GPU parallel accelerated source iteration method, and the former consumes 43.75% less memory compared to the latter. The convolutional neural network is mainly used as the virtual physics engine for the THFR digital twin system, in addition to solving the neutron diffusion spatiotemporal kinetics equation and further improving computational speed. The algorithm directly utilizes the neutron macroscopic cross-section of the material to calculate the neutron flux density distribution without using the lattice homogenization, providing theoretical guidance and algorithm support for developing the high-precision multi-physical field coupling model.