X-MeshGraphNet: Scalable Multi-Scale Graph Neural Networks for Physics Simulation

TL;DR

X-MeshGraphNet delivers a scalable, mesh-free surrogate for physics simulations by combining halo-based graph partitioning with gradient aggregation, CAD-derived graph construction from STL data, and multi-scale point-cloud graphs. This trio preserves full-graph training equivalence while enabling memory-efficient, real-time inference on large domains, demonstrated in automotive aerodynamics with high predictive accuracy ($R^2 \approx 0.94$) and strong memory/compute scaling advantages. The approach reduces reliance on meshing at inference, extends to UNet-like architectures, and exhibits superior strong scaling versus distributed all-to-all message passing on multi-GPU clusters. The work offers practical impact for real-time design and optimization across fluid dynamics and related physical simulations, with code available via NVIDIA Modulus.

Abstract

Graph Neural Networks (GNNs) have gained significant traction for simulating complex physical systems, with models like MeshGraphNet demonstrating strong performance on unstructured simulation meshes. However, these models face several limitations, including scalability issues, requirement for meshing at inference, and challenges in handling long-range interactions. In this work, we introduce X-MeshGraphNet, a scalable, multi-scale extension of MeshGraphNet designed to address these challenges. X-MeshGraphNet overcomes the scalability bottleneck by partitioning large graphs and incorporating halo regions that enable seamless message passing across partitions. This, combined with gradient aggregation, ensures that training across partitions is equivalent to processing the entire graph at once. To remove the dependency on simulation meshes, X-MeshGraphNet constructs custom graphs directly from tessellated geometry files (e.g., STLs) by generating point clouds on the surface or volume of the object and connecting k-nearest neighbors. Additionally, our model builds multi-scale graphs by iteratively combining coarse and fine-resolution point clouds, where each level refines the previous, allowing for efficient long-range interactions. Our experiments demonstrate that X-MeshGraphNet maintains the predictive accuracy of full-graph GNNs while significantly improving scalability and flexibility. This approach eliminates the need for time-consuming mesh generation at inference, offering a practical solution for real-time simulation across a wide range of applications. The code for reproducing the results presented in this paper is available through NVIDIA Modulus.

Figures (11)

• Figure 1: Illustration of the partitioning scheme with Halo on tesselated representation of a Koenigsegg car.
• Figure 2: An illustration of the geometry variation in samples 100, 300, and 500.
• Figure 3: Comparison between the predictions and the ground truth for pressure for Sample 320.
• Figure 4: Comparison between the predictions and the ground truth for wall shear stress for Sample 320.
• Figure 5: Comparison between the predicted and ground truth force in the flow direction. $R^2$ is $0.942$.