  Fluid mechanics is a fundamental field in engineering and science. Solving
the Navier-Stokes equation (NSE) is critical for understanding the behavior of
fluids. However, the NSE is a complex partial differential equation that is
difficult to solve, and classical numerical methods can be computationally
expensive. In this paper, we present an innovative approach for solving the NSE
using Physics Informed Neural Networks (PINN) and several novel techniques that
improve their performance. The first model is based on an assumption that
involves approximating the velocity component by employing the derivative of a
stream function. This assumption serves to simplify the system and guarantees
that the velocity adheres to the divergence-free equation. We also developed a
second more flexible model that approximates the solution without any
assumptions. The proposed models can effectively solve two-dimensional NSE.
Moreover, we successfully applied the second model to solve the
three-dimensional NSE. The results show that the models can efficiently and
accurately solve the NSE in three dimensions. These approaches offer several
advantages, including high trainability, flexibility, and efficiency.
