Learning Parameterized Coarse Mesh Dynamics of a Confined Cylinder Flow With Graph Neural Networks

Reduced-order models (ROMs) play a crucial role in making high-fidelity flow simulations computationally tractable for tasks such as optimization and control. In this work, we investigate a graph-based ROM using MeshGraphNets, a Graph Neural Network (GNN) architecture designed to learn physical dynamics on unstructured meshes. As a test case, we consider the unsteady flow past a confined cylinder across Reynolds numbers ranging from 100 to 1000, a canonical benchmark that exhibits increasingly complex vortex shedding behavior. Unlike prior studies that rely on fine-resolution meshes, we deploy the model on a significantly coarsened mesh with nodes placed near the cylinder wall as well as at sensor-relevant locations, and propose a metric based on the Earth Mover's Distance (EMD) in order to efficiently compare different test cases. Despite the coarse spatial and temporal resolution, the model captures key unsteady features such as drag fluctuations and reproduces spectral characteristics at sensor locations. We also identify regions in parameter space where prediction accuracy degrades, motivating strategies for dataset partitioning that substantially increase model performance. These results demonstrate the feasibility of using GNNs as data-driven ROMs for unsteady flow prediction.