“…In recent years, deep neural network (DNN), which reveals superior capability to process and to predict complicated systems, has been widely employed in a variety of fields, e.g., natural language processing 5 , computer vision 6 , etc. 7 , 8 Due to its high computational efficiency and scalability, especially on heterogeneous platforms, DNN has become a promising technique in scientific computing and even provides the possibility for real-time PDE solving 9 . Ray et al 10 proposed a neural network-based indicator to correct the irregular solution in the discontinuous Galerkin scheme.…”