  Feature propagation in Deep Neural Networks (DNNs) can be associated to
nonlinear discrete dynamical systems. The novelty, in this paper, lies in
letting the discretization parameter (time step-size) vary from layer to layer,
which needs to be learned, in an optimization framework. The proposed framework
can be applied to any of the existing networks such as ResNet, DenseNet or
Fractional-DNN. This framework is shown to help overcome the vanishing and
exploding gradient issues. Stability of some of the existing continuous DNNs
such as Fractional-DNN is also studied. The proposed approach is applied to an
ill-posed 3D-Maxwell's equation.
