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

在科学中，集成用于模拟来自各种来源的数据中的不确定性，包括测量误差、建模不准确和缺乏足够的采样。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，从医学到天气预报等。本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。这将使科学家通过发展新的见解和更快地发现，更好地理解他们领域内的现象。这些技术将在一个生物医学工程研究小组和一个研究小组的合作下进行测试，前者帮助开发新的挽救生命的心脏病治疗方法，后者帮助开发支持安全、清洁和可靠的国家能源网络的技术。此外，本计划将研究和提倡将更好的教学方法，如同行评审，纳入计算机科学课程。研究结果将通过课程材料（如设计迷你挑战）整合到可视化和计算几何课程中，并通过教学主题小组和研讨会等外展活动与教育界分享。为了完成项目的目标，拓扑数据分析工具为从集成中健壮地提取特征和设计可视化提供了强大的理论基础，以执行重要的不确定性分析任务，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：如何有效地利用拓扑从集成中提取特征；以及如何为领域专家设计可视化，从而有效地传达特征。为了从集成中提取特征，该项目将研究对多个集成实现的拓扑进行鲁棒比较和对比的新方法。然后，与领域科学家合作，它将设计新的可视化方法，以高效和有效地比较和探索集成内的特征和变化。项目网站提供了额外的信息，并将包括对开发工具、数据集和教育内容的访问。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。

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.