Generalization capabilities of MeshGraphNets to unseen geometries for fluid dynamics

TL;DR

This paper evaluates MeshGraphNets' ability to generalize to unseen geometries in fluid dynamics, introducing a new dataset and testing how well the model predicts flows around novel shapes.

Contribution

It presents a new CFD benchmark dataset with diverse shapes and assesses MeshGraphNets' generalization to unseen geometries, extending prior experiments.

Findings

MGNs can sometimes generalize well to different obstacle shapes

Training on one shape and testing on another shows promising results

New dataset enables better evaluation of geometric generalization in CFD

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.