Physics-Informed GNNs

Physics-informed graph neural networks use graph structure to represent meshes, networks, or interacting entities while incorporating known physical laws into learning. Common approaches include adding equation-residual or conservation losses, building physical operators directly into message passing, and combining learned components with numerical solvers or variational energy methods. These models are used as fast surrogates for tasks such as fluid and solid mechanics, power flow, and transport on irregular or changing topologies. A central challenge is ensuring that low prediction error also means physical consistency, while maintaining reliable transfer across new geometries, operating conditions, and system sizes.