Deficiencies, including inadequate precision and onerous computational processes, plague conventional techniques for predicting the aerodynamic characteristics of airfoils. This paper proposes a Physics-Informed Neural Network (PINN) model for airfoil aerodynamic characteristics, which can effectively improve these problems. Initially, a conventional BP neural network is configured to predict aerodynamic characteristics and assess the prediction error. Based on this, a PINN model is constructed by designing a loss function that integrates physical information. The PINN model introduces incompressible Navier-Stokes equation residuals, Mahalanobis-distance regularization terms, and angle-of-attack symmetry into the loss function, achieving a deep integration of data-driven and physical constraints. Concurrently, a comparison is made between the PINN model and the traditional model to assess the former's precision in predicting aerodynamic characteristics. Finally, the Non-dominated Sorting Genetic Algorithm (NSGA-II) is utilized to research airfoil optimization design, and the presented method is demonstrated to be effective in achieving a reasonable airfoil optimization design.