Generalization capabilities of MeshGraphNets to unseen geometries for fluid dynamics
This addresses the problem of generalization in data-driven computational fluid dynamics for researchers, but it is incremental as it extends prior work on MGNs and datasets.
The paper investigates how well MeshGraphNets (MGN) generalize to unseen geometries in fluid dynamics, such as predicting flow around new obstacles not in training data, and shows that MGNs can sometimes generalize well to different shapes when trained on one obstacle shape and tested on another.
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.