Abstract:Fluid flows can be theoretically described by the Navier−Stokes equations. However, due to the nonlinear convection term, analytical solutions of the equations can only be obtained for a few cases. For complex engineering flow problems at high Reynolds numbers, it is difficult to calculate the flow field efficiently and accurately by numerical simulation, and it is difficult to obtain rich details by experiment or field measurement. With the rapid development of artificial intelligence technology, data-driven technologies such as deep learning can make use of flexible network structures and efficient optimization algorithms to obtain strong approximating ability for high-dimensional and nonlinear problems, bringing opportunities for the development of computational methods for fluid mechanics. Different from traditional data-driven deep learning modeling methods for image classification and natural language processing, the flow fields predicted by deep learning models should obey physical laws of fluids, such as the Navier−Stokes equations and typical energy spectrum. Recently, physics-enhanced deep learning methods have developed rapidly and are gradually becoming a new research paradigm of fluid mechanics: the method of selecting network input features or designing network architecture according to the laws of fluid physics is called the physics-inspired deep learning method, and the method of explicitly integrating the laws of fluid physics into the network loss function or network architecture is called the physics-informed deep learning method. The research content covers the fields of reduced order modelling of fluid mechanics and solution of flow governing equations.