Deep Nitsche Method: Deep Ritz Method with Essential Boundary Conditions

We propose a new method to deal with the essential boundary conditions encountered in deep learning-based numerical solvers for partial differential equations. The trial functions representing by neural networks are non-interpolatory, which makes enforcement of nontrivial matter. Our resorts Nitsche's variational formulation this difficulty, is consistent, and does not require significant extra computational costs. prove error estimate energy norm illustrate on several representative problems posed at most 100 dimension.