3 papers
math.NA2026
Error Analysis of Tr-PINNs Algorithm for 2D Incompressible Navier-Stokes Equations with Non-Homogeneous Boundary Conditions
Dongjie Liu, Xuebo Li, Rong Yang
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. Ho…
math.DS2026
Global random attractor for 3D stochastic Navier-Stokes equation with nonlinear colored noise
Xingjie Yan, Rong Yang, Alain Miranville
In this paper, we first introduce the definitions of random evolutionary system that associate with random evolutionary semigroup and the corresponding global weak or strong random…
physics.flu-dyn2025
WAN3DNS: Weak Adversarial Networks for Solving 3D Incompressible Navier-Stokes Equations
Wenran Li, Xavier Cadet, Miloud Bessafi +7
The 3D incompressible Navier-Stokes equations model essential fluid phenomena, including turbulence and aerodynamics, but are challenging to solve due to nonlinearity and limited s…