TDOR-MPINNs: Multi-output physics-informed neural networks based on time differential order reduction for solving coupled Klein–Gordon–Zakharov systems

With the continuous development in the field of deep learning, in recent years, it has also been widely used in the field of solving partial differential equations, especially the physics-informed neural networks (PINNs) method. However, the PINNs method has some limitations in solving coupled Klein–Gordon–Zakharov (KGZ) systems. To this end, in this article, inspired by the PINNs method and combined with the characteristics of the coupled KGZ systems, we design a neural network model, named multi-output physics-informed neural networks based on time differential order reduction (TDOR-MPINNs), to solve the coupled KGZ systems. Compared with the PINNs, the TDOR-MPINNs first reduces the time derivatives, and thus can increase supervised learning tasks. And through comparing the numerical results obtained by using TDOR-MPINNs and PINNs for solving the one-dimensional (1-D) and two-dimensional (2-D) coupled KGZ systems, we further validate the effectiveness, accuracy and reliability of the TDOR-MPINNs.