The flow-induced vibration (FIV) of fluid-conveying pipes, caused by the interaction between internal flowing fluid and the structure, is a critical issue in engineering. In this paper, the data and physics driven deep learning (DL) models are established to solve the forward and inverse FIV problems, which are used to overcome the challenges of accuracy, efficiency and data requirements encountered by traditional single physics or data driven models. Based on the density variation model of slug flow, the vibration equation of the fluid-conveying pipe subjected to gas-liquid two-phase flow is derived. Subsequently, the incomplete FIV equation and discretely sparse data space are utilized to solve the solution space of the system and refine the physical equation. The established physics-informed deep learning (PIDL) model is used to learn the characteristics of the FIV system, enabling response prediction and unknown parameters inversion (the stiffness EI or fluid density ρin (x, t)). The findings that show the efficacy of the PIDL model in accurately predicting motion information and estimating unknown parameters of fluid-conveying pipe. By analyzing the responses and properties of the pipeline structure, it is possible to diagnose the service status of the pipeline and analyze the flow state of the fluid within.