基于PINN深度机器学习技术求解多维中子学扩散方程  

Solving Multi-Dimensional Neutron Diffusion Equation Using Deep Machine Learning Technology Based on PINN Model

作　　者：刘东[1,2,3] 罗琦 唐雷 安萍 杨帆[1] Liu Dong;Luo Qi;Tang Lei;An Ping;Yang Fan(Science and Technology on Reactor System Design Technology Laboratory,Nuclear Power Institute of China,Chengdu,610213,China;CNNC Engineering Research Center of Nuclear Energy Software and Digital Reactor,Chengdu,610213,China;Committee on Science and Technology of China National Nuclear Corporation,Beijing,100822,China)

机构地区：[1]中国核动力研究设计院核反应堆系统设计技术重点实验室,成都610213 [2]中核核能软件与数字化反应堆工程技术研究中心,成都610213 [3]中国核工业集团有限公司科技委,北京100822

出　　处：《核动力工程》2022年第2期1-8,共8页Nuclear Power Engineering

基　　金：第五批国家高层次人才特殊支持计划科技创新领军人才基金项目。

摘　　要：阐述了基于物理信息指引的神经网络模型(PINN),构造深度神经网络作为试函数,将其代入中子学扩散方程形成残差,并作为机器学习的加权损失函数,进而通过深度机器学习技术逼近中子学扩散方程数值解;针对扩散方程的特点,提出了特征值方程加速收敛方法、有效增殖系数(k_(eff))高效并行搜索技术、学习样本网格点不均匀分布策略等创新性关键技术,并对神经网络深度、神经元数量、边界条件损失函数权重等关键参数进行了敏感性分析。验证计算结果表明,该方法具有良好的精度,提出的关键技术具有显著的成效,为中子学扩散方程的数值求解探索出了新的技术途径。This paper elaborates the physics-informed neural network model(PINN),constructs a deep neural network as a trial function,substitutes it into the neutron diffusion equation to form a residual,and takes it as the weighted loss function of machine learning,and then approaches the numerical solution of the neutron diffusion equation by deep machine learning technique;According to the characteristics of diffusion equation,this paper puts forward innovative key technologies such as accelerated convergence method of eigenvalue equation,efficient parallel search technology of effective multiplication coefficient(k_(eff)),learning sample grid point uneven distribution strategy,and analyzes the sensitivity of key parameters such as neural network depth,neuron number,boundary condition loss function weight and so on.The verification calculation results show that the method has good accuracy,and the proposed key technology has remarkable results,and explores a new technical approach for the numerical solution of the neutron diffusion equation.

关 键 词：深度机器学习 基于物理信息指引的神经网络模型(PINN) 中子学扩散方程 加速收敛 有效增殖系数(k_(eff)) 

分 类 号：TL334[核科学技术—核技术及应用]