Poisson CNN: Convolutional neural networks for the solution of the Poisson equation on a Cartesian mesh

Understand

The Poisson equation is commonly encountered in engineering, for instance in computational fluid dynamics (CFD) where it is needed to compute corrections to the pressure field to ensure the incompressibility of the velocity field.

• In the present work, we propose a novel fully convolutional neural network (CNN) architecture to infer the solution of the Poisson equation on a 2D Cartesian grid with different resolutions given the right hand side term, arbitrary boundary conditions and grid parameters.
• It provides unprecedented versatility for a CNN approach dealing with partial differential equations.
• The boundary conditions are handled using a novel approach by decomposing the original Poisson problem into a homogeneous Poisson problem plus four inhomogeneous Laplace sub-problems.