Firstly, this study uses a partial differential equation to conduct experimental research on the teaching effect of music education. Secondly, the convolutional neural network method is used to optimize the weighted factors in the traditional finite volume method. This makes the calculation results of the model more accurate under the condition of coarse particles. It is found that the model can solve Burgers and level set equations accurately and effectively. This method can evaluate the teaching effect of music education more accurately and improve students’ learning products of music.