Generalization capabilities of MeshGraphNets to unseen geometries for fluid dynamics

TL;DR

This work probes whether MeshGraphNets (MGN) can generalize to unseen geometries in incompressible fluid dynamics. By extending the Cylinder Flow benchmark with multiple shapes and objects, the authors assess cross-geometry generalization using autoregressive MGN rollouts trained with denoising-like noise injection. Results show MGNs can produce physically reasonable, coarse-flow predictions on unseen shapes and often recover vortex patterns, though qualitative fidelity (especially vortex dynamics) degrades for shapes not present in training. The study demonstrates substantial speedups over traditional solvers (up to about 100x on GPUs) and highlights directions to improve generalization via larger models and more diverse geometry datasets. Overall, MGNs offer a promising, fast surrogate for multi-query CFD tasks with room for improvement in accurately capturing complex vortex structures across diverse geometries.

Abstract

This works investigates the generalization capabilities of MeshGraphNets (MGN) [Pfaff et al. Learning Mesh-Based Simulation with Graph Networks. ICML 2021] to unseen geometries for fluid dynamics, e.g. predicting the flow around a new obstacle that was not part of the training data. For this purpose, we create a new benchmark dataset for data-driven computational fluid dynamics (CFD) which extends DeepMind's flow around a cylinder dataset by including different shapes and multiple objects. We then use this new dataset to extend the generalization experiments conducted by DeepMind on MGNs by testing how well an MGN can generalize to different shapes. In our numerical tests, we show that MGNs can sometimes generalize well to various shapes by training on a dataset of one obstacle shape and testing on a dataset of another obstacle shape.

Figures (10)

• Figure 1: Domain of the Navier-Stokes benchmark problem (Cylinder Flow) dfg_benchmark
• Figure 2: High-level overview of how MGNs predict the next state given the current state $\bm{s}_k$.
• Figure 3: One example mesh from each of the five datasets.
• Figure 4: Plot of the Euclidean norm of the velocity field at the final time step for a FEM simulation (bottom) and the corresponding MGN prediction (top) of a mesh coming from the cylinder_stretch dataset. The prediction has an all-steps RMSE of circa $0.076$ and stems from an MGN that was trained on cylinder_stretch.
• Figure 5: Plot of the Euclidean norm of the velocity field at the final time step for two FEM simulations (bottom) and their corresponding MGN predictions (top) of two meshes coming from the standard_cylinder dataset. The prediction (a) has an all-steps RMSE of circa $0.193$ and (b) has an all-steps RMSE of circa $0.086$. Both predictions stem from an MGN that was trained on standard_cylinder.