Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks

Understand

In this paper, we introduce a new approach based on distance fields to exactly impose boundary conditions in physics-informed deep neural networks.

• The challenges in satisfying Dirichlet boundary conditions in meshfree and particle methods are well-known.
• This issue is also pertinent in the development of physics informed neural networks (PINN) for the solution of partial differential equations.
• We introduce geometry-aware trial functions in artifical neural networks to improve the training in deep learning for partial differential equations.