Competitive physics-informed networks for high-accuracy solutions to Navier-Stokes problems

Physics Informed Neural Networks (PINNs) represent partial differential equations (PDEs) as neural networks, solving these PDEs to an accuracy of around 10^-3 L₂ relative error via Adam-based optimizers. Competitive Physics Informed Neural Networks (CPINNs) were recently introduced by the authors to enable training to at least single-precision accuracy (10^-7). They are based on an adversarial approach to training, which amounts to a minimax optimization problem, that relaxes the poor conditioning of the differential operators that comprise the PDE. Here, we apply the CPINN strategy to solve canonical Navier-Stokes problems with high accuracy.