III: Small: Visualizing Robust Features in Vector and Tensor Fields

向量场和张量场为描述许多科学应用中的物理现象提供了一种强大的语言。在大气科学中，矢量用于表示具有速度和方向的空气运动，并捕获典型和非典型的大气条件。在材料科学中，应力和应变张量被用来描述材料体在经历变形时的行为，并促进材料强度的研究。该项目的主要目标是定义和量化向量和张量场中的鲁棒特征，并为知识发现提供科学有意义的可视化。鲁棒特征是在由测量噪声、数值不稳定性或模拟不确定性引起的数据的小扰动下稳定的对象、结构或感兴趣的区域。通过与领域科学家的密切合作，鲁棒特征被定义和评估，以帮助他们区分数据中的虚假结构和基本结构。在材料科学中，提取应力张量场中的鲁棒特征将有助于材料科学家更好地表征和预测3D开裂，以制造更强的材料。在神经科学中，量化脑成像中退化元素的鲁棒性将为疾病诊断的组织微观结构特征提供新的度量和可视化。在生物工程中，心脏中三维传导速度场的鲁棒涡流提取和跟踪将帮助生物工程师开发新的指标来检测和表征与心脏病发作相关的缺血性应激。在大气科学中，提取和可视化风数据的强大特征将有助于大气科学家建立对危险天气条件（如野火）的态势感知，并为消防人员提供野火天气预报和资源规划。这个项目也将提供一个独特的多学科活动环境，并为学生提供将可视化与科学应用相结合的训练机会。这个项目将建立一种基于特征的可视化的新方法，它有三个相互关联的目标。首先，它将推导出向量场和张量场及其集合的鲁棒特征的新颖数学公式。其次，它将在特征提取、跟踪、简化、视觉表示和不确定性可视化方面开发新的鲁棒性驱动算法。第三，它将通过与四个高影响力应用领域的科学家密切合作来应用和评估拟议的框架：材料科学、神经科学、生物工程和大气科学。通过在未破裂的多晶体中模拟微力学场，该项目将鲁棒性特征与可视化相结合，以提高微力学场的可解释性和疲劳失效表面的预测。利用来自人类连接组项目的弥散张量成像（DTI），该项目将研究交叉纤维的可量化特征，作为深部脑刺激器放置的长期目标的一部分。利用在猪和犬的组织中产生的3D传导速度，该项目将从漩涡的稳定性和演变中产生基于特征的特征，并从长远来看，将它们用于疾病诊断和医疗干预。利用高分辨率快速刷新模型（HRRR）生成的集成数据集，该项目将在大气模型的可视化和统计分析中使用强大的特征来识别非典型大气条件，以进行野火天气评估。研究结果将通过一系列研究论文和开源软件工具实例化，目标是合作科学家社区和大型研究社区。这些软件工具将在MIT或BSD许可下通过GitHub提供。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Vector and tensor fields provide a powerful language to describe physical phenomena in many scientific applications. In atmospheric sciences, vectors are used to represent air movements with speed and directions and to capture typical and atypical atmospheric conditions. In materials science, stress and strain tensors are used to specify the behaviors of material bodies experiencing deformations and to facilitate the study of material strength. The main objective of this project is to define and quantify robust features in vector and tensor fields and to derive scientifically meaningful visualization for knowledge discovery. Robust features are objects, structures, or regions of interest that are stable under small perturbations of the data that arise from measurement noise, numerical instability or simulation uncertainty. Robust features are defined and evaluated via close collaborations with domain scientists to help them discriminate spurious from essential structures in the data. In materials science, the extraction of robust features in stress tensor fields will help the materials scientists better characterize and predict 3D cracking for manufacturing stronger materials. In neuroscience, quantifying the robustness of degenerate elements in brain imaging will offer new metrics and visualization in characterizing tissue microstructure for disease diagnostics. In bioengineering, robust vortex extraction and tracking of 3D conduction velocity fields in the heart will help bioengineers develop new metrics that detect and characterize ischemic stress associated with a heart attack. In atmospheric sciences, extracting and visualizing robust features in wind data will help the atmospheric scientists establish situation awareness of hazardous weather conditions such as wildfires and to provide wildfire weather forecasting and resource planning for firefighting personnel. This project will also provide a unique environment for multidisciplinary activities and training opportunities for students in integrating visualization with scientific applications. This project will establish a new approach to feature-based visualization with three interconnected aims. First, it will derive novel mathematical formulations of robust features for vector and tensor fields and their ensembles. Second, it will develop new robustness-driven algorithms in feature extraction, tracking, simplification, visual representation, and uncertainty visualization. Third, it will apply and evaluate the proposed framework via close collaborations with scientists in four high-impact application areas: materials science, neuroscience, bioengineering, and atmospheric sciences. Using simulated micro-mechanical fields in an uncracked polycrystal, the project will integrate robust features with visualization to improve the interpretability of micro-mechanical fields and the prediction of fatigue-failure surfaces. Using diffusion tensor imaging (DTI) from the Human Connectome Project, the project will investigate quantifiable characteristics of crossing fibers as part of a long-term goal for deep brain stimulator placement. Using 3D conduction velocity generated in volumes of swine and canine tissues, the project will generate feature-based signatures from vortex stability and evolution and use them, in the long term, for disease diagnostics and medical intervention. Using ensemble datasets generated from the High-Resolution Rapid Refresh Model (HRRR), the project will use robust features in the visualization and statistical analysis of atmospheric models to identify atypical atmospheric conditions for wildfire weather assessment. The research results will be instantiated by a collection of research papers and open-source software tools targeting the communities of collaborating scientists and the large research community. These software tools will be made available via GitHub under MIT or BSD licenses.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.