PhyICNet: Physics-informed interactive learning convolutional recurrent network for spatiotemporal dynamics

The numerical solution of spatiotemporal partial differential equations (PDEs) using the deep learning method has attracted considerable attention in quantum mechanics, fluid mechanics, and many other natural sciences. In this paper, we propose an interactive temporal physics-informed neural network architecture based on ConvLSTM for solving spatiotemporal PDEs, in which the information feedback mechanism in learning is introduced between the current input and the previous state of network. Numerical experiments on four kinds of classical spatiotemporal PDEs tasks show that the extended models have superiority in accuracy, long-range learning ability, and robustness. Our key takeaway is that the proposed network architecture is capable of learning information correlation of the PDEs model with spatiotemporal data through the input state interaction process. Furthermore, our method also has a natural advantage in carrying out physical information and boundary conditions, which could improve interpretability and reduce the bias of numerical solutions.