Error estimates and physics informed augmentation of neural networks for thermally coupled incompressible Navier Stokes equations.

Physics Informed Neural Networks (PINNs) are shown to be a promising method for the approximation of partial differential equations (PDEs). PINNs approximate the PDE solution by minimizing physics-based loss functions over a given domain. Despite substantial progress in the application of PINNs to a range of problem classes, investigation of error estimation and convergence properties of PINNs, which is important for establishing the rationale behind their good empirical performance, has been lacking. This paper presents convergence analysis and error estimates of PINNs for a multi-physics problem of thermally coupled incompressible Navier-Stokes equations. Through a model problem of Beltrami flow it is shown that a small training error implies a small generalization error.

Déclaration de conflit d'intérêts

Declarations Conflicts of interest Authors have no competing interests.