VortexTransformer: End-to-End Objective Vortex Detection in 2D Unsteady Flow Using Transformers

Xingdi Zhang, Peter Rautek and Markus Hadwiger

Computer Graphics Forum (Proceedings of Eurographics 2025) , 2025

Vortex structures play a pivotal role in understanding complex fluid dynamics, yet defining them rigorously remains challenging. One hard criterion is that a vortex detector must be objective, i.e., it needs to be indifferent to reference frame transformations. We propose VortexTransformer, a novel deep learning approach using point transformer architectures to directly extract vortex structures from pathlines. Unlike traditional methods that rely on grid-based velocity fields in the Eulerian frame, our approach operates entirely on a Lagrangian representation of the flow field (i.e., pathlines), enabling objective identification of both strong and weak vortex structures. To train VortexTransformer, we generate a large synthetic dataset using parametric flow models to simulate diverse vortex configurations, ensuring a robust ground truth. We compare our method against CNN and UNet architectures, applying the trained models to real-world flow datasets. VortexTransformer is an end-to-end detector, which means that reference frame transformations as well as vortex detection are handled implicitly by the network, demonstrating the ability to extract vortex boundaries without the need for parameters such as arbitrary thresholds, or an explicit definition of a vortex. Our method offers a new approach to determining objective vortex labels by using the objective pairwise distances of material points for vortex detection and is adaptable to various flow conditions.

@article{Zhang2025VortexTransformer,
  title = {VortexTransformer: End-to-End Objective Vortex Detection in 2D Unsteady Flow Using Transformers},
  author = {Zhang, Xingdi and Rautek, Peter and Hadwiger, Markus},
  journal = {Computer Graphics Forum (Proceedings of Eurographics 2025)},
  year = {2025},
  volume = {to appear},
  number = {},
  pages = {}
}