物理信息神经网络对圆管内层流流动和换热的数值模拟验证与求解效率研究  

Numerical simulation validation and solution efficiency study of physics-informed neural network for laminar flow and heat transfer in circular tubes

作　　者：姚嘉晔 陈鹏飞 洪钢 张尧立 YAO Jiaye;CHEN Pengfei;HONG Gang;ZHANG Yaoli(College of Energy,Xiamen University,Xiamen 361102,China;Fujian Research Center for Nuclear Engineering,Xiamen 361102,China)

机构地区：[1]厦门大学能源学院,福建厦门361102 [2]福建省核能工程技术研究中心,福建厦门361102

出　　处：《厦门大学学报(自然科学版)》2025年第1期156-168,共13页Journal of Xiamen University:Natural Science

摘　　要：[目的]提出了一种将在标准条件下训练的权重和偏置信息加载到模型中的方法,以提升相邻条件下物理信息神经网络(physics-informed neural network,PINN)数值模拟效率.[方法]以二维圆管为对象,流动状态为稳态流动,控制方程为受重力影响的Navier-Stokes方程组,利用解析解对PINN模拟精度进行验证并对超参数进行敏感性分析,进而对圆管内层流流动换热过程进行数值模拟,并利用权重与偏置信息对邻近工况进行预测.[结果]PINN数值模拟具有可行性和准确性,与传统软件Fluent计算结果的相对误差约±5%.载入已有工况权重和偏置信息可以显著提高PINN数值模拟的效率,速度场与温度场同Fluent计算结果的相对误差均小于±5%.[结论]利用PINN可以对流体层流流动换热进行数值模拟,同时可以利用预训练的权重和偏置信息提高数值模拟效率.[Objective]Physics-informed neural network(PINN)has attracted great attention in the field of artificial intelligence due to their ability to bring interpretability to traditional machine learning and deep learning via embedding physical laws into the loss function.PINN exhibits a strong fitting ability for nonlinear problems,making them a promising tool for solving problems related to fluid mechanics and heat transfer.The numerical simulation of thermal fluids utilizing the meshless property of PINN has become a new hot trend in research.However,improving the efficiency of numerical solutions using PINN remains a key challenge that has attracted the attention of scholars.[Methods]In this study,a PINN-based numerical simulation solver for thermal fluids is coded with DeepXDE and other related libraries.Fluid flows steadily.The solver uses the Navier-Stokes system of equations as physical constraints,and boundary conditions are adopted to perform a complete numerical simulation process of the laminar flow and heat transfer of incompressible fluid.Sensitivity analysis of the hyperparameters is performed,and a vertical circular tube and a horizontal circular tube are selected as research objects for multi-operating condition solution,and the results are compared with those simulated by Fluent.The weights and biases of the numerical simulation results under this condition are used to predict and calculate the operating conditions under similar boundary conditions.[Results]The results indicate that sensitivity analysis of hyperparameters(neural network structure,learning rate and collocation points)is essential for effective numerical simulation using PINN,and appropriate hyperparameters have positive effects on numerical simulation results.The optimization effect of numerical simulation is positively correlated with the number of hidden layers and neurons.When the number of hidden layers is 6,the numerical simulation results tend to stabilize.When the number of neurons per layer reaches 50,the influence of hidden lay

关 键 词：物理信息神经网络 对流换热 数值模拟 

分 类 号：TP312[自动化与计算机技术—计算机软件与理论]