MomentumGNN: A graph neural network architecture designed to preserve linear and angular momentum when modeling deformable materials

Researchers propose MomentumGNN, a novel GNN (graph neural network — a type of AI that processes interconnected data) architecture that predicts per-edge stretching and bending impulses rather than unconstrained nodal accelerations, guaranteeing preservation of linear and angular momentum in dynamic simulations.

The model is trained in an unsupervised fashion using a physics-based loss function and outperforms baseline GNNs in scenarios where momentum plays a pivotal role, while retaining GNNs' ability to generalize to arbitrary shapes, mesh topologies, and material parameters.

The work addresses a gap in existing GNN architectures, which struggle to correctly predict the temporal evolution of key physical quantities such as linear and angular momentum despite their efficiency in modeling deformable materials.