Title: Deep neural network and numerical analysis – adversarial attack on image and videos

Abstract: Deep neural networks have achieved state-of-the-art performance in a variety of fields. The exponential growth of machine learning models and the extreme success of deep learning have seen application across a multitude of disciplines. Recent works observe that a class of widely used neural networks can be viewed as the Euler method of numerical discretization. From the numerical discretization perspective, Total Variation Diminishing (TVD) Runge-Kutta methods are more advanced techniques than the explicit Euler method that produce both accurate and stable solutions. Motivated by the TVD property and a generalized Runge-Kutta method, we proposed new networks which improve robustness against adversarial attacks. If time permits, we explore a deep learning methodology that can be applied to the data-driven discovery of numerical PDEs.