Abstract: A novel physics-informed neural network named PINN was proposed recently by Karniadakis G. E.(2017). It combined the neural network and partial differential equation to endow the traditional machine learning algorithm with prior knowledges and interpretability. Its performance has attracted lots of research interest, and this paper presents the predictions based on PINN and direct numerical simulation results for two cases. Combing the neural networks and compressible Navier-Stokes equations, the turbulent instantaneous flow field of a fully developed turbulent channel flow was reconstructed, a good agreement has been achieved between the DNS results and predictive results for both instantaneous and the statistical mean profiles of flow quantities. The method was also used to predict the undetermined coefficient of the N-S equation for the 2-dimensional circular cylinder and the undetermined item of the N-S equation for the 3-dimensional compressible channel flow with different initial values, the results matched the exact data very well. These results proved that the physics-informed neural network had a strong capability for physics problems.