Multi-domain physics-informed neural networks for solving transient heat conduction problems in multilayer materials

Abstract

In this paper, we aim to numerically resolve linear and nonlinear transient heat conduction problems in multilayer composite materials using a deep learning method called multi-domain physics-informed neural networks (MDPINNs). For this purpose, the multilayer media are first divided into independent sub-domains based on domain decomposition technique. The single-layer deep neural networks are first established, and each sub-domain has its corresponding sub-network. Then, each two sub-networks are connected by continuity conditions on the interface to form a MDPINNs’ framework that can directly solve the transient heat conduction problem in multilayer media. The temperature distribution in the computational domain can be obtained by training the MDPINNs, including the temperature values on the interface. A series of numerical experiments are carried out to verify that the proposed framework can achieve satisfactory accuracy, including in micrometer or even nanometer structures. Compared with conventional methods, the MDPINNs have the advantage of directly solving both linear and nonlinear heat conduction problems in multilayer materials in a unified and concise form.