基于物理融合神经网络的广义对流扩散方程格子Boltzmann求解研究  

Research on Lattice Boltzmann Solution of Generalized Convection Diffusion Equation Based on Physical Fusion Neural Network

作　　者：王亚辉 肖豪 马宇 谢宇辰 池泓航 Wang Yahui;Xiao Hao;Ma Yu;Xie Yuchen;Chi Honghang(Sino-French Institute of Nuclear Engineering and Technology,Sun Yat-Sen University,Zhuhai,Guangdong,519082,China)

机构地区：[1]中山大学中法核工程与技术学院,广东珠海519082

出　　处：《核动力工程》2025年第2期56-67,共12页Nuclear Power Engineering

基　　金：国家自然科学基金(12205389);广东省基础与应用基础研究基金(2022A1515011735、2025A1515011855)。

摘　　要：为提高深度学习方法的网络复用性,构建一种适应于不同控制方程和不同物性参数条件的深度网络模型,本研究提出了基于物理融合神经网络的格子Boltzmann方法(PFNN-LBM)。在格子Boltzmann框架下建立了不同特征控制方程的统一格式离散速度Boltzmann方程,并使用单一网络的参数化物理信息约束神经网络求解,可以在一次训练后同时求解不同形式和不同物理参数的控制方程。为测试PFNN-LBM的准确性和适应性,选取了四种典型非线性对流扩散方程开展预测分析,包括扩散方程、非线性导热方程、SineGordon方程和Burgers-Fisher方程,同时测试了不同物理参数条件的预测性能并对双群中子扩散问题进行了测试。计算结果表明,所提出的PFNN-LBM可以在一次训练后高精度地求解不同形式和不同物理参数的控制方程。这项工作可以为高效灵活地求解不同类型的方程提供一个新的框架,对于工程应用中的多物理场耦合计算方面可能具有突出优势。In order to improve the network reusability of the deep learning method and construct a deep network model suitable for different control equations and different physical parameters,a lattice Boltzmann method based on physical fusion neural network(PFNN-LBM)is proposed in this study.The unified discrete-velocity Boltzmann equation for equations with different characteristics is established under lattice Boltzmann method,and solved using the parameterize physics–informed neural network with a single network.The PFNN-LBM can simultaneously solve governing equations with different forms and different physical parameters within one single training.In order to test the accuracy and adaptability of PFNN-LBM,four types of macro-equations,including diffusion equation,nonlinear heat conduction equation,Sine-Gordon equation and Burgers-Fisher equation,are selected for prediction analysis.At the same time,the prediction performance under different physical parameters and the two-group neutron diffusion equations are tested.The calculation results show that the proposed PFNN-LBM can solve the control equations of different forms and different physical parameters with high accuracy after one training.This work can provide a novel framework for solving different types of equations efficiently and flexibly,and for engineering application,this work may have outstanding advantages in multi-physics coupling calculations.

关 键 词：物理信息约束神经网络 格子BOLTZMANN 深度学习 非线性对流扩散方程 

分 类 号：TL334[核科学技术—核技术及应用]