Abstract:
In this paper, the physical-informed neural networks (PINN) is used to solve the multi-media nonlinear transient heat conduction problem. According to the thermophysical parameters of multi-media, the computational domain is divided into multiple sub-domains, and a tailored PINN is applied in each sub-domain. The PINNs in the sub-domains are connected by the flux continuity of the common interface between the these sub-domains. To formulate the PINN framework, a loss function is constructed based on the residuals arising from the governing partial differential equations (PDEs), initial conditions, boundary conditions, and the continuity conditions at the interfaces between the subdomains. The methodology employs the automatic differential algorithm to accurately compute the partial derivatives of temperature with respect to various input variables present in the PDEs. The gradient of loss function with respect to the weight and deviation is calculated by the chain derivation method, and then the network parameters are updated according to the gradient descent method. In order to accelerate the convergence of the network, the training hyperparameter is introduced into the activation function and the network is adaptive by adjusting the slope of the activation function. The study evaluates the versatility and effectiveness of the PINN framework in addressing the multi-medium nonlinear transient heat conduction problem. Additionally, it investigates the influences of various factors, including different activation functions, learning rates, network structures, and the weights of components within the loss function, on the output results of the PINN. The results indicate that PINN exhibits high reliability and a straightforward solving process when addressing multi-media nonlinear transient heat conduction problems. Moreover, it does not require artificial preprocessing of the solution domain, demonstrating a significant level of practicality for engineering applications. Through systematic theoretical analysis and a series of numerical examples, the article thoroughly illustrates the robustness of PINN as a potent tool for solving complex heat conduction problems.