{"title":"Physics-informed neural networks for modeling steady-state heat conduction","authors":"V. A. Glazunov, A. P. Koroleva, M. A. Nesterov","doi":"10.1134/S0869864325010287","DOIUrl":null,"url":null,"abstract":"<div><p>The paper presents the results of research on the application of physics-informed neural networks (PINN) for solving the steady state heat conduction equation. The solutions of the heat conduction equation with boundary conditions of I, II and III kinds, and also taking into account the presence of a heat source are considered. Formulations of heat conduction problems and error functions for one-dimensional and two-dimensional cases are given. The proposed neural network is implemented using PyTorch and DeepXDE frameworks. Based on the import of mesh data from the digital product “Logos Heat”, the possibility of using geometry of arbitrary type is provided. The influence of the neural network architecture and the choice of the activation function on the obtained results is investigated. Numerical experiments for the proposed method are carried out on one-dimensional and two-dimensional problems having exact and known numerical solution.</p></div>","PeriodicalId":800,"journal":{"name":"Thermophysics and Aeromechanics","volume":"32 1","pages":"23 - 33"},"PeriodicalIF":0.6000,"publicationDate":"2026-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Thermophysics and Aeromechanics","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1134/S0869864325010287","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"ENGINEERING, AEROSPACE","Score":null,"Total":0}
引用次数: 0
Abstract
The paper presents the results of research on the application of physics-informed neural networks (PINN) for solving the steady state heat conduction equation. The solutions of the heat conduction equation with boundary conditions of I, II and III kinds, and also taking into account the presence of a heat source are considered. Formulations of heat conduction problems and error functions for one-dimensional and two-dimensional cases are given. The proposed neural network is implemented using PyTorch and DeepXDE frameworks. Based on the import of mesh data from the digital product “Logos Heat”, the possibility of using geometry of arbitrary type is provided. The influence of the neural network architecture and the choice of the activation function on the obtained results is investigated. Numerical experiments for the proposed method are carried out on one-dimensional and two-dimensional problems having exact and known numerical solution.
期刊介绍：
The journal Thermophysics and Aeromechanics publishes original reports, reviews, and discussions on the following topics: hydrogasdynamics, heat and mass transfer, turbulence, means and methods of aero- and thermophysical experiment, physics of low-temperature plasma, and physical and technical problems of energetics. These topics are the prior fields of investigation at the Institute of Thermophysics and the Institute of Theoretical and Applied Mechanics of the Siberian Branch of the Russian Academy of Sciences (SB RAS), which are the founders of the journal along with SB RAS. This publication promotes an exchange of information between the researchers of Russia and the international scientific community.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
