PHYSICS-INFORMED ENCODER-DECODER GATED RECURRENT NEURAL NETWORK FOR SOLVING TIME-DEPENDENT PDES

The ability of deep-learning approaches to approximate complex functions offers a promising alternative for solving partial differential equations (PDEs). The methodology of incorporating the physics prior to the deep neural network can significantly reduce the requirement for labeled data. In this study, a novel physics-informed encoder-decoder gated recurrent units neural network is proposed to solve the time-dependent PDEs without using any observed data. The encoder is utilized to approximate the underlying patterns and structures of solutions over the entire spatial-temporal domain. The approximated solution is processed by the decoder, which is the gated recurrent units layer. We utilize the initial condition as the initial state of the gated recurrent units to retain critical information in the hidden states. The boundary conditions are enforced in the final prediction to enhance the model's performance. Then, we incorporate physical laws into the neural network during the training process. The effectiveness of this algorithm is demonstrated by solving BurgersFisher and coupled two-dimensional burgers' equations. The ability to identify unknown parameters is demonstrated through the solution of inverse problems.