With the continuous development of the computer field, the Internet has become the main way of education in today's era. The development of computer technology and big data has brought innovation and opportunities to the teaching mode of ideological and political courses in colleges and universities. Due to the dynamic change of big data, there are many difficulties in the establishment of ideological and political course models in colleges and universities. This paper studies the innovation of ideological and political course modes in colleges and universities on the network platform under the background of big data. This paper mainly compares the traditional teaching mode and explores the formal modeling method of network platform education. The discrete dynamic modeling technology of the complex system is used to model the formal process of online education. Then, it carries out nonlinear prediction modeling for the operation efficiency and traffic change of the network platform under the big data environment and uses dynamic modeling to predict the learning effect of college students' ideological and political course mode. The results show that the formal method of education under dynamic modeling can improve the defects of traditional teaching and give full play to the advantages of network platform teaching. Improving the teaching mode of network platform can improve students' learning efficiency. Finally, in the dynamic model prediction, the problem of big data affecting the model results is improved, and the accuracy of the prediction model is improved.