标题： 具有独立高斯不确定性的二维矢量场局部发散的概率可视化高效方法 显示英文标题

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

摘要： 本工作专注于可视化二维矢量场局部发散的不确定性。 发散是流体流动的基本属性之一，因为它可以帮助领域科学家分析流动中源（正发散）和汇（负发散）的位置。 然而，矢量场数据中的固有不确定性可能导致错误的发散计算，对后续分析产生不利影响。 尽管蒙特卡洛（MC）采样是估计发散不确定性的经典方法，但它随着数据规模和样本数量的增加而面临收敛缓慢和可扩展性差的问题。 因此，我们提出了两项贡献，以解决MC方法在收敛速度和可扩展性方面的挑战。 (1) 我们推导出一种闭式方法，用于高效且准确地可视化局部发散的不确定性，假设矢量不确定性独立服从高斯分布。 (2) 我们进一步将我们的方法集成到Viskores中，这是一个平台可移植的并行库，以加速不确定性可视化。 在我们的结果中，我们展示了我们的串行解析方法（加速比高达1946X）和并行Viskores（加速比高达19698X）算法相对于经典串行MC方法的显著效率和准确性的提升。 我们还展示了我们的概率发散可视化相比传统均值场可视化在定性上的改进，后者忽略了不确定性。 我们在风向预测和海洋模拟数据集上验证了我们方法的准确性和效率。 显示英文摘要

摘要： 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.