In the past few years, many scholars gradually began to interpret the conventional residual neural Networks (ResNet) as the partial differential equations. Some scholars called it Neural PDE. Ruthotto, Haber, Lin and others have done relevant researches on this interpretation. This paper mainly studies the residual neural network model driven by the heat equation (HERN) and the convection-diffusion equation (CDERN). Experiment I and experiment II mainly used these two networks mentioned above to compare with the traditional ResNet for image recognition under the interference of the Gaussian noise and the salt and pepper noise. In experiment III, under the interference of the Gaussian noise, the HERN model and the CDERN model are used to compare with the denoising effects of the traditional ResNet, the Gaussian filtering algorithm and Perona-Malik Model. The results show that the denoising effect of the Gaussian noise with the square error greater than 0.6 based on the HERN model is better than Gaussian filter, the CDERN model and the traditional ResNet model; In addition, it also shows that CDERN and HERN are more stable than the traditional ResNet.