  The finite element method, finite difference method, finite volume method and
spectral method have achieved great success in solving partial differential
equations. However, the high accuracy of traditional numerical methods is at
the cost of high efficiency. Especially in the face of high-dimensional
problems, the traditional numerical methods are often not feasible in the
subdivision of high-dimensional meshes and the differentiability and
integrability of high-order terms. In deep learning, neural network can deal
with high-dimensional problems by adding the number of layers or expanding the
number of neurons. Compared with traditional numerical methods, it has great
advantages. In this article, we consider the Deep Galerkin Method (DGM) for
solving the general Stokes equations by using deep neural network without
generating mesh grid. The DGM can reduce the computational complexity and
achieve the competitive results. Here, depending on the L2 error we construct
the objective function to control the performance of the approximation
solution. Then, we prove the convergence of the objective function and the
convergence of the neural network to the exact solution. Finally, the
effectiveness of the proposed framework is demonstrated through some numerical
experiments.
