Predicting the nonlinear dynamics of spatiotemporal PDEs via physics-informed informer networks

Partial differential equations (PDEs) have been widely used in physics, engineering, finance, and other fields to simulate various real-world phenomena. Recent advances in deep learning have shown the great potential of physics-informed neural networks as a novel machine learning model that combines deep learning with the laws of physics. However, most of the existing PINNs methods based on fully connected neural networks only focus on the spatial connection of the loss function of low-dimensional space–time, which constitutes an inherent limitation. To this end, coupled neural networks of Informer and PINNs called PhyInformer are proposed, which take into account the dependencies of data on time and space. The loss function is defined as the residuals of the discretized PDEs together with its boundary value condition loss and initial value condition loss. Extensive numerical experiments on four different models (e.g., 2D-Burgers’ equations, 2D-Diffusion equations and Allen–Cahn equations and Wave equations). Demonstrate that our proposed method significantly outperforms existing PINNs.