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.

翻译：本研究探讨了MeshGraphNets（MGN）[Pfaff等人，《基于图网络的网格模拟学习》，ICML 2021]在流体动力学中对未见几何结构的泛化能力，例如预测训练数据中未出现过的新障碍物周围的流场。为此，我们创建了一个新的数据驱动计算流体动力学（CFD）基准数据集，该数据集通过包含不同形状和多个物体扩展了DeepMind的圆柱绕流数据集。随后，我们利用该新数据集扩展了DeepMind在MGN上进行的泛化实验，通过测试MGN对不同形状的泛化性能来评估其能力。数值实验表明，通过在单一障碍物形状的数据集上进行训练，并在另一障碍物形状的数据集上进行测试，MGN有时能够对各种形状展现出良好的泛化能力。