Abstract: This paper adopts an extension of the traditional adaptive mesh refinement (AMR) method, speeifically combining physics-informed neural networks (PINNs) with the residuals of the Navier-Stokes equations, which describe incompressible fluids as the refinement metric, to guide the refinement of unstructured triangular meshes. We first solve the flow field corresponding to a coarse mesh by the traditional finite volume method, and then integrate the flow field data from the physical model to train PINNs. The trained model is used to predict the residuals of the Navier-Stokes equations at the center of the coarse mesh cells, and a fixed number of mesh cells with the largest residuals are selected, which are refined using the Delaunay refinement algorithm based on the constraint of the maximum area of the mesh cells. The mesh is refined by repeating the above steps cyclically until the physical quantity of interest converges with the number of meshes. In the incompressible airfoil flow scenario with Re=1000, compared to the traditional AMR framework in Fluent, the lift-drag coefficients obtained from the optimization of this framework are in good agreement with the reference solution, but the number of optimal mesh cells after refinement is significantly reduced.