Table 2.

List of Deep Neural Networks, their associated Differential Equation Numerical schemes

Deep neural network	Associated differential equation	Numerical scheme
Residual neural network(ResNet)	$\frac{\partial u}{\partial t}=f\left(u\right)$	Euler’s forward
Deep PolyNet	$\frac{\partial u}{\partial t}=f\left(u\right)$	Euler’s backward
Ultra-DNN(FractalNet)	$\frac{\partial u}{\partial t}=f\left(u\right)$	Runga-Kutta(RK)
Reversible Residual Network(RevNet)	$\dot{X}=f(\dot{Y)}\text{and}\dot{Y}=f(\dot{X)}$	Euler’s forward