What is a graph neural network (GNN)?
Definition
A graph neural network (GNN) is a neural network that operates on graphs: nodes connected by edges. In engineering simulation, the mesh becomes the graph, and the GNN predicts quantities such as velocity, pressure or displacement by passing learned messages between neighboring nodes, so it works directly on irregular meshes.
Example
MeshGraphNets (ICLR 2021) turns a simulation mesh into a graph and learns the dynamics by passing messages between neighboring nodes, with published results in aerodynamics, structural mechanics and cloth. On very fine meshes, information needs many message-passing steps to cross the domain, which multiscale variants address by also passing messages on a coarser mesh.
Sources
- Pfaff, Fortunato, Sanchez-Gonzalez, Battaglia, "Learning Mesh-Based Simulation with Graph Networks," ICLR 2021, arxiv.org/abs/2010.03409
- Fortunato, Pfaff, Wirnsberger, Pritzel, Battaglia, "MultiScale MeshGraphNets," 2022, arxiv.org/abs/2210.00612