Learning time-dependent PDE solver using Message Passing Graph Neural Networks

Understand

One of the main challenges in solving time-dependent partial differential equations is to develop computationally efficient solvers that are accurate and stable.

• Here, we introduce a graph neural network approach to finding efficient PDE solvers through learning using message-passing models.
• We first introduce domain invariant features for PDE-data inspired by classical PDE solvers for an efficient physical representation.
• Next, we use graphs to represent PDE-data on an unstructured mesh and show that message passing graph neural networks (MPGNN) can parameterize governing equations, and as a result, efficiently learn accurate solver schemes for linear/nonlinear PDEs.