The typical large sweep angle wing laminar flow design of supersonic aircraft faces the problem of boundary layer transition induced by crossflow instability. The standard e ^N method based on linear stability theory involves solving eigenvalue problems and requires frequent interactive operations， which cannot meet the needs of fast transition prediction and iterative design. To address the above difficulties， a linear stability analysis is conducted on the similarity solution of the three-dimensional compressible boundary layer to generate a large number of eigenvalue samples. The powerful spatial feature extraction ability of convolutional layers is utilized to achieve automatic recognition of the input baseflow profile features， and together with the flow parameters and disturbance parameters at the outer edge of the boundary layer， they are mapped to eigenvalue or local growth rates through fully-connected layers， thus constructing an e ^N convolutional neural network model suitable for predicting the instability and transition of supersonic stationary crossflow waves. By conducting stability analysis on a series of variable operating conditions and geometries of infinite swept wings， the neural network model’s prediction results of disturbance amplification factors are in good agreement with the standard e ^N method. Finally， based on the stability analysis and flight test data of a supersonic swept wing crossflow transition model developed by NASA， the neural network model’s ability to predict transition in real three-dimensional configurations was verified. The results showed that this model has strong generalization ability and ensures high accuracy， making it a relatively simple and reliable modeling method.