参数化物理内嵌神经网络求解稳态单能中子扩散解集

Solving Steady-state Mono-energy Neutron Diffusion Solution Setwith Parameterized Physics-informed Neural Network

物理内嵌神经网络(PINN)是一种结合了物理学知识的深度学习方法,近年开始被用于计算核工程领域中的堆芯中子问题。然而,PINN在求解不同问题时的网络不可复用性极大地影响了该方法的使用价值和效率。为了解决网络不可复用性问题,提出了一种基于参数化PINN的方法,开发了一种新型的中子扩散物理方程的代理模型。该代理模型具有很高的灵活性和效率,可以在无样本的前提下,快速给出任意给定参数中子扩散问题的解。此外,比较了边界软约束和硬约束下参数化PINN的代理模型预测精度。最后,验证了硬约束PINN代理模型相较于有限元计算软件的加速能力。结果表明,硬约束下的PINN代理模型具有更高的预测精度,且加速比在1000以上。

Physics-Informed Neural Network(PINN)is a deep learning method that incorporates physical knowledge.It has recently been applied to solve core neutron problems in computational nuclear engineering.However,the non-reusability of PINNs when solving different problems greatly hampers its value and efficiency.To address this issue,a method based on parameterized PINNs has been proposed,leading to the development of a new surrogate model for the neutron diffusion physical equation.This surrogate model is highly flexible and efficient,capable of quickly providing solutions to any given parameter neutron diffusion problem without the need for sample data.Furthermore,the predictive accuracy of the parameterized PINN surrogate model under soft and hard boundary constraints was compared.The results show that the PINN surrogate model under hard constraints has higher predictive accuracy,and the acceleration ratio is over 1000.This work primarily focuses on the application of PINNs to core neutron problems in computational nuclear engineering.The goal is to improve the reusability of PINNs,thereby enhancing their value and efficiency in computational nuclear engineering.Based on parameterized PINNs,this work has drawn several conclusions through the study of single-region,double-region,and triple-region examples.The parameterized PINN neutron diffusion surrogate model proposed in this paper has high accuracy.When compared with the reference solution,the relative error of the single-region three-physical-parameter example can reach 0.07%,the double-region five-physical-parameter example can reach 1%,and the triple-region three-physical-parameter example can reach 2%.The predictive accuracy of the parameterized PINN neutron diffusion surrogate model under hard boundary constraints is significantly higher than that of the parameterized PINN under soft boundary constraints.The accuracy of the two differs by 1-2 orders of magnitude.The parameterized PINN neutron diffusion surrogate model under hard boundary constraints has a very obvious acceleration effect compared to the reference program COMSOL.The acceleration ratios for the three examples are 1923.4,1396.1,and 1385.1,respectively.This work can be applied to the rapid solution of complex neutron diffusion problems.Future work will focus on further optimizing this method based on parameterized PINNs to improve its performance in handling more complex problems.In addition,the possibility of applying this method to other physical problems will be explored to fully utilize its advantages in handling complex problems.At the same time,this work has also found some problems in the parameterized PINN method,such as the obvious spatial distribution characteristics of errors in the triple-region example.In the future,research will be conducted on how to better handle potential outliers to further improve the robustness of the model.