  Deep neural networks are an attractive alternative for simulating complex
dynamical systems, as in comparison to traditional scientific computing
methods, they offer reduced computational costs during inference and can be
trained directly from observational data. Existing methods, however, cannot
extrapolate accurately and are prone to error accumulation in long-time
integration. Herein, we address this issue by combining neural operators with
recurrent neural networks, learning the operator mapping, while offering a
recurrent structure to capture temporal dependencies. The integrated framework
is shown to stabilize the solution and reduce error accumulation for both
interpolation and extrapolation of the Korteweg-de Vries equation.
