Efficient Probabilistic Visualization of Local Divergence of 2D Vector Fields with Independent Gaussian Uncertainty

• URL: http://arxiv.org/abs/2510.01190v1
• Date: Thu, 21 Aug 2025 18:16:17 GMT
• Title: Efficient Probabilistic Visualization of Local Divergence of 2D Vector Fields with Independent Gaussian Uncertainty
• Abstract summary: Divergence is one of the fundamental attributes of fluid flows.<n>Uncertainty inherent in vector field data can lead to erroneous divergence computations.<n>We present a two-fold contribution that tackles the challenges of slow convergence and limited scalability of the Monte Carlo sampling approach.
• Score: 3.2999490997091265
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This work focuses on visualizing uncertainty of local divergence of two-dimensional vector fields. Divergence is one of the fundamental attributes of fluid flows, as it can help domain scientists analyze potential positions of sources (positive divergence) and sinks (negative divergence) in the flow. However, uncertainty inherent in vector field data can lead to erroneous divergence computations, adversely impacting downstream analysis. While Monte Carlo (MC) sampling is a classical approach for estimating divergence uncertainty, it suffers from slow convergence and poor scalability with increasing data size and sample counts. Thus, we present a two-fold contribution that tackles the challenges of slow convergence and limited scalability of the MC approach. (1) We derive a closed-form approach for highly efficient and accurate uncertainty visualization of local divergence, assuming independently Gaussian-distributed vector uncertainties. (2) We further integrate our approach into Viskores, a platform-portable parallel library, to accelerate uncertainty visualization. In our results, we demonstrate significantly enhanced efficiency and accuracy of our serial analytical (speed-up up to 1946X) and parallel Viskores (speed-up up to 19698X) algorithms over the classical serial MC approach. We also demonstrate qualitative improvements of our probabilistic divergence visualizations over traditional mean-field visualization, which disregards uncertainty. We validate the accuracy and efficiency of our methods on wind forecast and ocean simulation datasets.

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