Analysis of Power-Law Fin-Type Problems using Physics Informed Neural Networks

Abstract This study aims to model the temperature distribution in a single fin subjected to steady one-dimensional heat conduction with nonlinear thermal behavior. For the modeling and solution of the problem, the Physics-Informed Neural Networks (PINNs) architecture was used. The temperature-dependent heat conduction problem and the nonlinear boundary conditions of this problem were formulated with a differential equation. With the help of the PINN architecture, the loss function was minimized in order to reduce the difference between the true value and the predicted value. During this minimization process, the PINN architecture was forced to be consistent with the physical laws. The results obtained after training the PINN architecture exhibit successful performance in terms of accuracy and reliability when compared with the results in the literature. These findings highlight the potential of PINNs as a powerful alternative to conventional methods for solving complex nonlinear heat conduction problems.