  There has been an arising trend of adopting deep learning methods to study
partial differential equations (PDEs). In this paper, we introduce a deep
recurrent framework for solving time-dependent PDEs without generating large
scale data sets. We provide a new perspective, that is, a different type of
architecture through exploring the possible connections between traditional
numerical methods (such as finite difference schemes) and deep neural networks,
particularly convolutional and fully-connected neural networks. Our proposed
approach will show its effectiveness and efficiency in solving PDE models with
an integral form, in particular, we test on one-way wave equations and system
of conservation laws.
