摘要
基于物理信息约束的神经网络(PINN)是一种将物理方程和机器学习结合的方法,近年来已成为研究热点之一。神经网络的训练是求解中子扩散方程不可或缺的步骤,为提高训练效率,参考源迭代法的思想将解联立方程变换为解多个单群方程,使用多个神经网络并行训练代替复杂的单一神经网络进行通量密度预测。对于有效增殖系数(k_(eff))搜索中出现的迭代次数多,收敛速度慢等问题,利用方程残差判断系统状态调整方程特征参数实现k_(eff)逐步搜索。在搜索过程中结合边界软约束和硬约束特点,使用边界硬约束扩展搜索范围,利用边界软约束逐步搜索,可以在无外部数据的前提下利用有限的迭代次数,实现高效快速的keff搜索。对上述方法采用了多个算例验证了可行性,计算结果表明,利用合理的训练程序,使用该方法获得数值解具有较好的精度。
The physics-informed neural network(PINN)is a method that combines physical equations with machine learning and has become one of the research hotspots in recent years.The training of neural networks is an indispensable step in solving the neutron diffusion equation.To improve training efficiency,the idea of the source iteration method is referred to,transforming the solution of the coupled equations into solving multiple single-group equations,and using multiple neural networks for parallel training instead of a complex single neural network for flux density prediction.To address the issues of numerous iterations and slow convergence speed in search for the effective multiplication coefficient(ker),the system state is adjusted by judging the equation residuals and modifying the equation eigenvalues to achieve a stepwise search for kefr-During the search process,by combining the characteristics of soft and hard boundary constraints,the hard boundary constraints are used to expand the search range,and the soft boundary constraints are used for gradual searching.This approach can achieve efficient and rapid ker search with limited iterations without external data.Multiple numerical examples have been used to verify the feasibility of the above method,and the calculation results show that using a reasonable training procedure,the numerical solutions obtained by this method have good accuracy.
作者
孙延鹏
马续波
SUN Yanpeng;MA Xubo(School of Nuclear Science and Engineering,North China Electric Power University,Beijing 102206,China)
出处
《核科学与工程》
北大核心
2025年第4期642-650,共9页
Nuclear Science and Engineering
关键词
神经网络
机器学习
PINN
中子扩散方程
有效增殖系数
Neural network
Machine learning
PINN
Neutron diffusion equation
Effective multiplication factor
