Construction of innovation and entrepreneurship teaching capacity in colleges and universities and its optimization path based on differential equation modeling

The rapid development of information and artificial intelligence technology has brought new opportunities for innovation and transformation in higher education, leading to innovative applications of data-driven-assisted teaching decisions. This paper analyzes the equilibrium point in predicting students’ performance using nonlinear differential equations, solves the expected value of students’ performance, and constructs a prediction model for students’ innovation and entrepreneurship performance. Student achievement data and characteristics are preprocessed to improve the accuracy of the prediction model. Based on Pearson’s coefficient, students’ innovation and entrepreneurship achievement are significantly correlated with teaching ability (P<0.05). The results show that, after implementing innovation and entrepreneurship teaching based on this prediction model, the predicted achievement of students in the intervention group is significantly higher than that of students in the control group (P<0.05). In the actual achievement test, the average total grade for the innovative entrepreneurship course of students in the intervention group was about 4.68-8.78 points higher than that of students in the control group. The achievement prediction model developed in this paper, along with the proposed optimization path for building innovation and entrepreneurship teaching capacity, offers significant guidance for the teaching research department in implementing effective teaching interventions and in the development of innovation and entrepreneurship education.