  In this work, we generalize the reaction-diffusion equation in statistical
physics, Schr\"odinger equation in quantum mechanics, Helmholtz equation in
paraxial optics into the neural partial differential equations (NPDE), which
can be considered as the fundamental equations in the field of artificial
intelligence research. We take finite difference method to discretize NPDE for
finding numerical solution, and the basic building blocks of deep neural
network architecture, including multi-layer perceptron, convolutional neural
network and recurrent neural networks, are generated. The learning strategies,
such as Adaptive moment estimation, L-BFGS, pseudoinverse learning algorithms
and partial differential equation constrained optimization, are also presented.
We believe it is of significance that presented clear physical image of
interpretable deep neural networks, which makes it be possible for applying to
analog computing device design, and pave the road to physical artificial
intelligence.
