摘要
基于物理信息神经网络(physics-informed neuralnetworks,PINN)求解非线性瞬态热传导问题并识别随温度变化的导热系数。首先,基于热传导问题的控制方程,利用初始条件和边界条件,构建损失函数。然后,应用自动微分算法求解控制方程中温度的偏导数。使用梯度下降算法,更新网络参数,最小化损失函数,实现热传导正问题的求解,并讨论了不同隐藏层数、神经元数量和域内数据点数量对计算结果的影响。最后,采用PINN识别随温度变化的导热系数,利用控制方程、测量温度和计算温度的残差构建损失函数,通过梯度下降算法,更新网络参数和导热系数,使其逼近于精确解,并比较了不同的测点数量和测量误差对计算结果的影响。结果表明,PINN能够有效求解非线性瞬态热传导问题并识别与温度相关的导热系数。
This study proposes a physics-informed neural networks(PINN)approach to solve transient nonlinear heat conduction problems and estimate the temperature-dependent thermal conductivity.First,a loss function is formulated using the residuals of partial differential equation,initial conditions,and boundary conditions specific to heat conduction.Then,automatic differentiation is applied to compute the temperature’s partial derivatives within the equation.The heat conduction problem is solved by minimizing the loss function through a gradient descent algorithm,which updates the network parameters.The influences of varying the number of hidden layers,neurons and interior collection points on the results are also examined.Finally,the PINN is applied to identify temperature-dependent thermal conductivities by formulating a loss function that includes residuals from the governing equation,measured temperature,and computed temperature.The network parameters and thermal conductivity values are updated by gradient descent algorithm to approximate the true solution.Additionally,the influences of different measurement points and errors on the results are compared.The findings show that the proposed method effectively solves transient heat conduction problems and accurately estimates temperature-dependent thermal conductivity.
作者
陈豪龙
唐欣越
柳兆涛
周焕林
CHEN Haolong;TANG Xinyue;LIU Zhaotao;ZHOU Huanlin(School of Civil Engineering,Hefei University of Technology,Hefei 230009,P.R.China)
出处
《重庆大学学报》
CAS
CSCD
北大核心
2024年第12期124-136,共13页
Journal of Chongqing University
基金
国家自然科学基金(12002181)
中央高校基本科研业务费(JZ2022HGQA0165,JZ2022HGTB0243)。
关键词
反问题
热传导问题
导热系数识别
物理信息神经网络
自动微分算法
inverse problems
heat conduction
thermal conductivity estimation
physics-informed neural networks
automatic differentiation
