Before revision:  We propose a deep learning algorithm similar in spirit to Galerkin methods, using a deep neural network instead of linear combinations of basis functions. The PDE is approximated with a deep neural network , which is trained on random batches of spatial points to satisfy the differential operator  and boundary conditions.
After revision:  We propose to solve high-dimensional PDEs by approximating the solution with a deep neural network , which is trained on random batches of spatial points to satisfy the differential operator and boundary conditions.