Error Analysis of Tr-PINNs Algorithm for 2D Incompressible Navier-Stokes Equations with Non-Homogeneous Boundary Conditions

Physics-informed neural networks (PINNs) have been widely applied to solve Navier-Stokes equations by enforcing outputs and gradients of deep models to satisfy target equations. However, conventional PINNs only constrain the boundary terms by means of the $L^2$-norm when addressing the equations with non-homogeneous boundary conditions. This single constraint strategy may cause inaccurate boundary simulation, further resulting in the decline of prediction accuracy. To resolve this critical issue, this paper proposes an improved physics-informed neural network by correcting the error of the boundary value, which is called Tr-PINNs. Based on the results of nonhomogeneous Stokes problem, the algorithm error analysis of Tr-PINNs is established. The efficacy of the Tr-PINNs algorithm is demonstrated via numerical experiments, which further demonstrate that the Tr-PINNs algorithm achieves a remarkable improvement in computational accuracy.

Source: arXiv:2606.06268v1 - http://arxiv.org/abs/2606.06268v1 PDF: https://arxiv.org/pdf/2606.06268v1 Original Link: http://arxiv.org/abs/2606.06268v1