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Abstract <p>The direct problem for the type III Green–Naghdi heat conduction equation is considered. This equation describes the propagation of thermal perturbations at finite velocity and takes the inertial effects of the heat flux into account. The numerical method is based on physics-informed neural networks (PINNs), which combine deep learning with a priori information regarding the structure of the differential equation. With specified thermal conductivity, the evolution of the temperature field in a uniform medium is simulated, taking account of the initial and boundary conditions. The network is trained on collocation points generated within the region at the boundary, so as to ensure that the approximation is consistent with the initial physical model. The results of the numerical experiment confirm the high accuracy and stability of the method in solving the hyperbolic problem. Comparison of the solution with the analytical result permits quantitative assessment of the neural network’s accuracy when the training set is limited.</p>

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Physics-Informed Neural Network for Solving the Type III Green–Naghdi Heat Conduction Equation

  • 期刊论文

  • 发表日期：

    2025年10月1日

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  • Ya. A. Vakhterova,
  • L. N. Rabinskiy

摘要

Abstract

The direct problem for the type III Green–Naghdi heat conduction equation is considered. This equation describes the propagation of thermal perturbations at finite velocity and takes the inertial effects of the heat flux into account. The numerical method is based on physics-informed neural networks (PINNs), which combine deep learning with a priori information regarding the structure of the differential equation. With specified thermal conductivity, the evolution of the temperature field in a uniform medium is simulated, taking account of the initial and boundary conditions. The network is trained on collocation points generated within the region at the boundary, so as to ensure that the approximation is consistent with the initial physical model. The results of the numerical experiment confirm the high accuracy and stability of the method in solving the hyperbolic problem. Comparison of the solution with the analytical result permits quantitative assessment of the neural network’s accuracy when the training set is limited.