Finite difference physics-informed neural networks enable improved solution accuracy of the Navier-Stokes equations

Abstract

Generating an accurate solution of the Navier--Stokes equations using physics--informed neural networks (PINNs) for higher Reynolds numbers in the corners of a lid--driven cavity problem is challenging. In this paper, we improve the solution accuracy of the incompressible Navier--Stokes equations in the region near the walls significantly and generate accurate secondary vortices in the corners of the lid--driven cavity by solving the governing equations using finite difference--based PINNs (FD--PINNs) without employing the known solution. We adopt the domain decomposition method (DDM) and combine it with the FD--PINNs to solve the lid--driven cavity problem for the Reynolds numbers Re = 400 and Re=1000. A comparison of the mean square error (MSE) between the presented and standard FD--PINNs using the reference solution is exhibited, showing the accuracy and effectiveness of the new approach.