Encoder–Decoder ConvLSTM Structure with Skip Connections for Solving Time-Dependent Partial Differential Equation

This paper proposes an efficient deep encoder–decoder ConvLSTM neural network for solving time-dependent differential partial equations. The encoder is composed of convolution layers, and the decoder is composed of transposed convolution layers, where the image is converted from low frequency to high frequency, and then back to low frequency in order to extract the spatial features of the partial differential equation. To accurately capture temporal information of time-dependent partial differential equations, ConvLSTM is configured in the encoder and decoder to solve the long-term evolution of dynamic systems. Furthermore, skip connections are added between the convolutional layer and the corresponding transposed convolutional layer, which not only overcomes the problem of gradient disappearance but also ensures that the underlying features are learned, enhancing the accuracy and efficiency of our network. Finally, the proposed network has been used to solve heat equations, wave equations, 2D Burgers equations, and high-order equations, and the results show that the present neural network has much better performance in terms of accuracy and efficiency.