Abstract This paper presents a simple yet principled approach to boosting the robustness of the residual network (ResNet) that is motivated by a dynamical systems perspective. Namely, a deep neural network can be interpreted using a partial differential equation, which naturally inspires us to characterize ResNet based on an explicit Euler method. This consequently allows us to exploit the step factor h in the Euler method to control the robustness of ResNet in both its training and generalization. In particular, we prove that a small step factor h can benefit its training and generalization robustness during backpropagation and forward propagation, respectively. Empirical evaluation on realworld datasets corroborates our analytical findings that a small h can indeed improve both its training and generalization robustness