  In this paper, we study the partial differential equation models of neural
networks. Neural network can be viewed as a map from a simple base model to a
complicate function. Based on solid analysis, we show that this map can be
formulated by a convection-diffusion equation. This theoretically certified
framework gives mathematical foundation and more understanding of neural
networks. Moreover, based on the convection-diffusion equation model, we design
a novel network structure, which incorporates diffusion mechanism into network
architecture. Extensive experiments on both benchmark datasets and real-world
applications validate the performance of the proposed model.
