An Implicit GNN Solver for Poisson-like problems

arXiv:2302.10891v3 Announce Type: replace
Abstract: This paper presents $\Psi$-GNN, a novel Graph Neural Network (GNN) approach for solving the ubiquitous Poisson PDE problems with mixed boundary conditions. By leveraging the Implicit Layer Theory, $\Psi$-GNN models an "infinitely" deep network, thus avoiding the empirical tuning of the number of required Message Passing layers to attain the solution. Its original architecture explicitly takes into account the boundary conditions, a critical prerequisite for physical applications, and is able to adapt to any initially …

abstract arxiv cs.ai cs.lg gnn graph graph neural network layer math.ap mixed network neural network novel paper solver theory type