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This research seeks to propose an innovative mathematical approach for measuring student performance in engineering education. This paper also includes a detailed analysis and the numerical solutions to this mathematical model. The designed mathematical model is constructed upon four categories, average candidates, weak candidates, below average candidates and good candidates. For the numerical results of the designed nonlinear mathematical model, the analysis through the Adams numerical scheme is applied for solving the differential system based on the migration rate and average student rate moves to weak and above average. Moreover, artificial neural network is also applied to get the stochastic results ANNs-LMB, also known as Levenberg-Marquardt training algorithm. The ANNs-LMB procedures have been implemented with three samples of data scales using the authentication, testing and training, which are chosen as 75%, 15% and 10%, respectively. According to the findings, when the rate of students leaving engineering studies increased, good students performed better, and when the rate of students below average moved, it was due to an increase in the rate of migration above average, the performance of the good students was only impacted in this way. This research material can be used in different designs and models to improve the students’ performance.