CAREER: A Measure Theoretic Framework for Topology-Based Visualization

由于计算设施的能力不断增强，由多物理模拟产生的数据，如二元黑洞合并和流体动力学，经历了指数级的增长。与此同时，数据密集型科学依赖于空间和时间分辨率不断提高的数据的获取、管理、分析和可视化。这个项目开发了一套新的方法来支持科学数据可视化中的核心任务(如特征跟踪、事件检测、集成分析和交互可视化)，以一种使用测量理论更能反映潜在物理的方式。结果将通过一组开放源码软件工具进行实例化，这些工具将为材料科学和高性能计算领域的合作科学家以及更大的研究社区部署。该项目利用几何测量理论、信息论和传输理论的工具进行基于拓扑的可视化，它利用拓扑概念来描述、简化和组织数据，以便科学地理解和交流。该项目侧重于两个技术组成部分。第一个组件将拓扑描述符表示为配备了概率度量的度量空间，该度量空间通过物理量、信息量化和比较分析来支持其丰富。第二个组件使用信息和传输理论来实现针对时变数据和集合的各种可视化任务。该项目将对应标准与最优运输的优化过程结合起来，以了解感兴趣的特征的演变；将事件检测中的不确定性与几何测量相结合；以及利用公制测量空间的统计来指导交互式可视化。研究人员与科学家密切合作，使用来自天体物理、材料科学和机械工程的数据来评估和调整框架，以更好地反映潜在的物理学。该项目为本科生和研究生提供了一个独特的多学科活动和培训机会的环境。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Data generated from multiphysics simulations, such as binary black hole mergers and fluid dynamics, have experienced exponential growth because of the growing capabilities of computing facilities. At the same time, data-intensive science relies on the acquisition, management, analysis, and visualization of data with increasing spatial and temporal resolutions. This project develops a new set of approaches to support the core tasks in scientific data visualization (such as feature tracking, event detection, ensemble analysis, and interactive visualization) in a way that is more reflective of the underlying physics using measure theory. The results will be instantiated by a collection of open-source software tools to be deployed for the collaborating scientists in materials science and high-performance computing, and the larger research community. This project leverages tools from geometric measure theory, information theory, and transportation theory for topology-based visualization, which utilizes topological concepts to describe, reduce and organize data for scientific understanding and communication. The project focuses on two technical components. The first component represents topological descriptors as metric spaces equipped with probability measures, which supports their enrichments with physical quantities, information quantification, and comparative analysis. The second component uses information and transportation theory to enable a wide variety of visualization tasks for time-varying data and ensembles. The project couples correspondence criteria with optimization processes from optimal transport to understand the evolution of features of interest; incorporates uncertainty in event detection with geometric measures; as well as utilizes statistics of metric measure spaces to guide interactive visualization. The investigator works closely with scientists using data from astrophysics, materials science, and mechanical engineering to evaluate and tune the framework to better reflect the underlying physics. This project provides a unique environment for multidisciplinary activities and training opportunities for undergraduate and graduate students.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.