重庆大学学报2024，Vol.47Issue(12)：124-136,13.DOI:10.11835/j.issn.1000-582X.2023.265
基于物理信息神经网络的非线性瞬态热传导正/反问题研究
Solving nonlinear transient heat conduction forward/inverse problem using physics-informed neural networks
摘要
Abstract
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.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Key words
inverse problems/heat conduction/thermal conductivity estimation/physics-informed neural networks/automatic differentiation分类
数理科学引用本文复制引用
陈豪龙,唐欣越,柳兆涛,周焕林..基于物理信息神经网络的非线性瞬态热传导正/反问题研究[J].重庆大学学报,2024,47(12):124-136,13.基金项目
国家自然科学基金(12002181) （12002181）
中央高校基本科研业务费(JZ2022HGQA0165,JZ2022HGTB0243). Supported by National Natural Science Foundation of China(12002181)and Fundamental Research Funds for the Central Universities(JZ2022HGQA0165,JZ2022HGTB0243). （JZ2022HGQA0165,JZ2022HGTB0243）
