Multi-domain physics-informed neural network for solving forward and inverse problems of steady-state heat conduction in multilayer media

In this paper, a novel deep learning technique, called multi-domain physics-informed neural network (M-PINN), is presented to solve forward and inverse problems of steady-state heat conduction in multilayer media. By adopting the domain decomposition technique, the multilayer media is first divided into several sub-domains. Then, the fully connected neural network is employed to approximate the temperature field on each sub-domain. Finally, a large total network framework is formed by combining subnetworks of all the mediums and using continuity conditions on interfaces. By training the total network, we can obtain the temperature distribution over the whole computational domain, including the interface between every two mediums. In the proposed method, the boundary conditions are introduced into the loss function, and the governing equation is used as a constrain item, which ensures the accuracy and stability of numerical approximation. As a meshless collocation technology, the M-PINN does not require tedious procedures such as meshing and numerical integration, and can freely address forward and inverse problems of thin body and coating structure. Several numerical examples are given to illustrate the efficiency and performance of the new method. Results indicate that the Swish and the Sigmoid functions are two better activation functions for such problems. As the number of nodes increases, the number of hidden layers does not need to be increased. Even for the thin film at nanoscale, the M-PINN still obtains accurate results. Moreover, the proposed scheme shows better performance than the traditional boundary element method in solving nonlinear heat conduction problems.