Modeling flow around a body in a two-dimensional channel using physics-informed neural networks

This paper presents several aspects of the application of physics-informed neural networks using the example of a two-dimensional steady-state problem of flow around an obstacle, modeled by the Navier–Stokes equations. The influence of the activation function, quantitative parameters of the training dataset, adaptive regularization, and adaptive meshing on the quality and accuracy of the solutions is investigated within a fixed neural network architecture. The interrelation between these factors and the modeling quality is analyzed to identify optimal conditions for improving the accuracy and stability of the solutions.