ABSTRACT

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.

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