CAREER: Discovering Structure in Uncertainty: Using Topology for Interactive Visualization of Uncertainty

在科学中，集合用于对来自各种来源的数据中出现的不确定性进行建模，包括测量误差，建模不准确以及缺乏足够的采样。了解这些错误对于提高人类对许多科学领域现象的理解至关重要，从城市规划到天体物理学到医学到天气预报等，该项目研究新的拓扑数据分析和可视化方法来分析不确定数据。这将使科学家能够通过开发新的见解和更快地发现来更好地了解其领域内的现象。这些技术将与一个生物医学工程研究团队合作进行测试，该团队帮助开发新的心脏病挽救生命的治疗方法，并帮助开发支持安全，清洁和可靠的国家能源网的技术。此外，该项目将研究和倡导将同行评议等更好的教学方法纳入计算机科学课程。研究结果将通过课程材料（如设计小挑战）纳入可视化和计算几何课程，并通过以教学为主题的小组讨论和讲习班等外联活动与教育界分享。拓扑数据分析工具为从集合中稳健地提取特征和设计可视化以执行重要任务提供了强有力的理论基础不确定性分析任务，包括识别和排序相似性，识别和排序变化，以及关联拓扑特征。该项目解决了两个重要的科学问题：如何有效地使用拓扑从集合中提取特征;以及如何为领域专家设计可视化，以有效地传达特征。为了从集成中提取特征，该项目将研究鲁棒地比较和对比多个集成实现的拓扑结构的新方法。然后，与领域科学家合作，它将设计新的可视化方法，以有效地比较和探索集成中的特征和变化。该项目的网站提供了更多的信息，并将包括访问开发的工具，数据集和教育内容。这个奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

In science, ensembles are used to model uncertainties that occur in data from a variety of sources, including errors in measurements, inaccuracies in modeling, and a lack of adequate sampling. Understanding these errors is critical to improving human understanding of phenomena in many areas of science, from urban planning to astrophysics to medicine to weather forecasting, etc. This project investigates new Topological Data Analysis and visualization methods to analyze uncertain data. This will enable scientists to better understand phenomena within their domain by developing new insights and making discoveries more quickly. The techniques will be tested in collaboration with a biomedical engineering research team helping to develop new life-saving treatments for heart attacks and a research team helping to develop technologies that support a safe, clean, and reliable national energy grid. Furthermore, this project will study and advocate for integrating better teaching methodologies, such as peer review, into computer science curricula. The results will be integrated into visualization and computational geometry courses through course materials, such as design mini-challenges, and shared with the educational community through outreach activities, such as pedagogy-themed panels and workshops.To accomplish the goals of the project, the tools of Topological Data Analysis provide a strong theoretical basis for robustly extracting features from ensembles and designing visualizations for performing important uncertainty analysis tasks, including identifying and ranking similarities, identifying and ranking variations, and correlating topological features. This project addresses two important scientific questions: how to effectively use topology to extract features from ensembles; and how to design visualizations for domain experts that efficiently communicate the features. To extract features from an ensemble, the project will investigate new methods of robustly comparing and contrasting the topology of multiple ensemble realizations. Then, in collaboration with domain scientists, it will design new visualization methods for efficiently and effectively comparing and exploring the features and variations within ensembles. The project web site provides additional information and will include access to developed tools, data sets, and educational content.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.