  This study aims to overcome the conventional deep-learning approaches based
on convolutional neural networks, whose applicability to complex geometries and
unstructured meshes is limited due to their inherent mesh dependency. We
propose novel approaches to improve mesh-agnostic spatio-temporal prediction of
transient flow fields using graph U-Nets, enabling accurate prediction on
diverse mesh configurations. Key enhancements to the graph U-Net architecture,
including the Gaussian mixture model convolutional operator and noise injection
approaches, provide increased flexibility in modeling node dynamics: the former
reduces prediction error by 95\% compared to conventional convolutional
operators, while the latter improves long-term prediction robustness, resulting
in an error reduction of 86\%. We also investigate transductive and
inductive-learning perspectives of graph U-Nets with proposed improvements. In
the transductive setting, they effectively predict quantities for unseen nodes
within the trained graph. In the inductive setting, they successfully perform
in mesh scenarios with different vortex-shedding periods, showing 98\%
improvement in predicting the future flow fields compared to a model trained
without the inductive settings. It is found that graph U-Nets without pooling
operations, i.e. without reducing and restoring the node dimensionality of the
graph data, perform better in inductive settings due to their ability to learn
from the detailed structure of each graph. Meanwhile, we also discover that the
choice of normalization technique significantly impacts graph U-Net
performance.
