Convection-Diffusion Equation: A Theoretically Certified Framework for
  Neural Networks
Tangjun Wang Chenglong Bao Zuoqiang Shi
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.