PA_CasualLSTM: A new time series prediction network with the physical constraint and adjusted Fourier neural operator for the time-dependent partial differential equation

In this work, a new time series prediction network is proposed in the framework of CasualLSTM with physical constraints and an adjusted Fourier neural operator (FNO) for the solution of the time-dependent partial differential equation. The framework of CasualLSTM is employed to learn the time evolution of spatial features which strengthens the extrapolation capability. With the help of adjusted Fourier layers (AFLs), residual connection, and the adaptive time-marching strategy, the network can quickly converge and extrapolate without labeled data by encoding PDE constraints into loss functions. Two examples, namely, Burger’s equation and two-dimensional Navier–Stokes (N-S) equation are used to evaluate the proposed method. Numerical results show that the proposed method has a good performance in solution accuracy and extrapolability.