Fourier filter-based physics- information convolutional recurrent network for 2D incompressible flow

Abstract

Physics-informed convolutional recurrent network (PhyCRNet) can solve partial differential equations without labeled data by encoding physics constraints into the loss function. However, the finite-difference filter makes the solution of 2D incompressible flow challenging. Hence, this paper proposes a Fourier filter-based physics-informed convolution recurrent network (named Fourier filter-based PhyCRNet), which replaces the finite-difference filter in PhyCRNet with the Fourier filter to solve the 2D incompressible flow problem. The suggested network improves the accuracy of the partial derivatives, solves the inverse Laplacian operator, and has similar generalization ability due to inheriting the framework of PhyCRNet. Four examples, including the 2D viscous Burger, FitzHugh–Nagumo RD, vorticity and the two-dimensional Navier- Stokes (N-S) equations, validate the correctness and reliability of the proposed Fourier filter-based PhyCRNet.