DeepPropNet - A recursive deep neural network propagator for learning evolutionary PDE operators

In this paper, we propose a deep neural network approximation to the evolution operator for time-dependent PDE systems over long time period by recursively using one single neural network propagator, in the form of POD-DeepONet with built-in causality feature, for a small time interval.The trained DeepPropNet of moderate size is shown to give accurate prediction of wave solutions over the whole time interval.