HI-MeshGraphNets Boosts Physics Simulation Accuracy and Efficiency

This paper introduces Hierarchical Interpolating MeshGraphNets (HI-MGN), an advanced graph neural network architecture designed to enhance the efficiency and accuracy of machine-learned physical surrogate models. Traditional GNNs struggle with large, high-fidelity meshes because information propagates slowly, requiring deep networks for long-range interactions, which increases computational burden and memory usage. HI-MGN overcomes these limitations by replacing the standard "flat" message processor with a hierarchical, multi-scale approach. It coarsens graphs using techniques like farthest-point sampling and Voronoi partitioning, while carefully preserving the original mesh topology. This allows messages to travel over greater geometric distances with fewer layers, mitigating issues like over-smoothing. A crucial component is a learned graph interpolation network that reconstructs fine-resolution features from the coarse graph representations. Across various structural and fluid dynamics benchmarks, HI-MGN demonstrated superior accuracy compared to existing MeshGraphNets and other multi-scale GNNs, while also significantly reducing training time and peak memory consumption. This framework offers a practical solution for scalable, mesh-based physics modeling.