MULTI-OUTPUT PHYSICS-INFORMED NEURAL NETWORKS MODEL BASED ON THE RUNGE-KUTTA METHOD

Physics-informed neural networks (PINN) have attracted considerable attention in the field of intelligent scientific computing primarily due to their capacity to incorporate prior knowledge of physics. This outstanding integration allows PINNs to automatically satisfy physical constraints even with limited or zero labeled data. As a result, the applicability and effectiveness of PINN are vastly developed across numerous domains. However, it is worth noting that the discrete time models of PINN, also known as PINN-RK, face a significant limitation in their ability to approximate multiple physical quantities and solve coupled partial differential equation systems simultaneously. This shortcoming hinders its ability to handle complex multi-physics fields, which is a crucial drawback in various practical scenarios. To overcome this limitation, a multi-output physics-informed neural network based on Runge-Kutta method (MO-PINN-RK) is proposed in this paper.MO-PINN-RK, building upon the success of PINN-RK, incorporates a sophisticated parallel neural network architecture, boasting multiple output layers for enhanced performance and accuracy. By associating each output layer with a sub-network and assigning it with different physical quantities, MO-PINN-RK can accurately solve the coupled partial differential equation system and predict multiple physical quantities simultaneously. The MO-PINN-RK proposed in this paper overcomes the limitation of PINN-RK that is only applicable to one dimensional problems extending its applicability to more general multi-dimensional problems. To demonstrate the effectiveness of MO-PINN-RK, it is then applied to the flow field prediction and parameter identification of flow around a cylinder. The outcomes unequivocally reveal that MO-PINN-RK surpasses PINN in terms of flow field prediction precision, achieving an enhancement of no less than 2 times. At the same time, MO-PINN-RK reduces the relative error by an order of magnitude in the context of parameter identification. This highlights the exceptional capabilities of MO-PINN-RK in the field of fluid dynamics, offering a more accurate and efficient solution for solving complex problems. © 2023 Chinese Journal of Theoretical and Applied Mechanics Press. All rights reserved.