VortexViz: Finding Vortex Boundaries by Learning from Particle Trajectories

TL;DR

VortexViz reframes vortex boundary extraction by learning from particle trajectories (flowlines) rather than solely from velocity components. It employs a two-branch DL model that processes a flowline-derived binary image and an information vector encoding swirl, fusing CNN and FCN features to decide if a seed point lies inside a vortex, trained with binary cross-entropy. Experiments on five unsteady 2D datasets show superior $F_1$ scores compared with threshold-based and velocity-based DL baselines, and demonstrate robustness to noise and applicability to real-world data such as Hurricane Dorian. The study also analyzes information-vector choices, flowline type, and integration settings, offering practical guidance and releasing code in supplementary materials to advance flow visualization research.

Abstract

Vortices are studied in various scientific disciplines, offering insights into fluid flow behavior. Visualizing the boundary of vortices is crucial for understanding flow phenomena and detecting flow irregularities. This paper addresses the challenge of accurately extracting vortex boundaries using deep learning techniques. While existing methods primarily train on velocity components, we propose a novel approach incorporating particle trajectories (streamlines or pathlines) into the learning process. By leveraging the regional/local characteristics of the flow field captured by streamlines or pathlines, our methodology aims to enhance the accuracy of vortex boundary extraction.

Figures (11)

• Figure 1: Particle Trajectories (pathlines and streamlines) Behave Differently Inside and Outside of a Vortex: In this paper, we exploit this behavior difference and physical properties of the flow field along the trajectory to find vortex boundaries. (Two streamlines from Jung93 are shown with a red cross indicating the seed point.)
• Figure 2: VortexViz Pipeline: Each flowline is represented as a binary image and an information vector. The binary image is processed by a convolutional Neural Network (CNN) and the information vector is processed by a Fully Connected Neural Network (FCN). The intermediate output layers of both these networks are merged. The merged layer is then used to predict if the seed point that originated the flowline is classified as inside a vortex or not.
• Figure 3: Visualizing Binary Images and Information Vectors: The top half of the figure shows binary image representations of particle trajectories. Notice that binary images exhibit notable disparities for particle trajectories inside (IN) and outside (OUT) of a vortex. The lower half showcases information vector representations of particle trajectories. These information vectors, presented as stacked values in heatmap form, illustrate differences among vectors of equal length. The information vectors initiate from the bottom of the heatmap, aligned with the hollow circle indicating the seed point of the example particle trajectory. Notice that each type of information vector is also different for particle trajectories inside (IN) and outside (OUT) the vortex. These visual differences lead us to believe these representations can be used to detect vortices.
• Figure 4: Qualitative Comparison with Other Methods. The first row displays the LIC image. Rows $2$-$5$ exhibit the output of IVD, Q, $\Omega$, and $\Delta$ criteria. Rows $6$-$9$ showcase the output of deep learning methods that learn from velocity components. The second-to-last row presents the output of our method, while the last row depicts the ground truth. Notice that our method can visualize vortices even where other methods fail.
• Figure 5: Understanding what Deep Learning Methods Learn from Velocity Components using Grad-cam: In the first row, we display images of a goldfish and a bear. The warmer sections within the overlaid heatmap depict the specific features learned by a CNN. Notably, these features correspond directly to the appearances of the goldfish and bear in the images. In the second row, we illustrate a counterclockwise and a clockwise vortex. The warmer regions within the overlaid heatmap reveal the features interpreted by a CNN as indicative of a vortex. It's worth observing that these highlighted features do not align with the vortex core. This observation leads us to hypothesize that what the CNN learns does not necessarily relate to the vortex itself.