CAREER: A Measure Theoretic Framework for Topology-Based Visualization

Award Number and Duration

NSF IIS 2145499

June 15, 2022 to May 31, 2027 (Estimated)

PI and Point of Contact

Bei Wang
Associate Professor
School of Computing and Scientific Computing and Imaging Institute
University of Utah
beiwang AT sci.utah.edu
http://www.sci.utah.edu/~beiwang

Overview

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.

Broader Impacts

This project provides a unique environment for multidisciplinary activities and training opportunities for undergraduate and graduate students. The research will be used to enhance course materials in computational topology, data visualization, and scientific computing, and more importantly, to promote visualization as a core part of training in data science. The PI will improve the impact and accessibility of education via her public YouTube channels. The project results will help the students discover how new and advanced data visualization tools offer analytics capabilities for large and complex data. This project will have a large impact on application domains via multidisciplinary collaborations in materials sciences and high performance computing.

Publications and Manuscripts

Presentations, Educational Development and Broader Impacts

1. Session Chairs, full paper session and Young Researchers Forum at the International Symposium on Computational Geometry (SOCG), June 11-14, 2024.

2. Invited Talk: Department of Computer Science, Aarhus University, May 31, 2024.
   Capturing Robust Topology in Data.
   
   
3. Invited Talk: NII Shonan Meeting on Advancing Visual Computing in Materials Science, Japan, May 14, 2024.
   Topological Data Analysis for Materials Science: A Hypergraph Perspective.
   
   
4. Invited Talk: Data Science and Applied Topology Seminar at the City University of New York, April 5, 2024.
   Reeb Graphs and Measure Theoretic Variants.
   
   
5. Overview Talk: Dagstuhl Seminar 24092: Applied and Combinatorial Topology, Dagstuhl, Germany, Feb 26, 2024.
   Reeb Graphs and Their Variants: Theory and Application.
   
   
6. Invited Talk: MPI Geometry Seminar, Max Planck Institute for Mathematics in the Sciences, Berlin, Germany, Jan 23, 2024.
   Reeb Graphs and Measure Theoretic Variants: Theory and Applications.
   
   
7. Invited Talk: MATH+ Workshop on Small Data Analysis, Zuse Institute Berlin (ZIB), Leipzig, Germany, Jan 17, 2024.
   Reeb Graphs and Measure Theoretic Variants: Theory and Applications.
   
   
8. Invited Talk: Computational Topology and Application Workshop at Tsinghua Sanya International Mathematics Forum (TSIMF), Dec 18, 2023.
   Measure Theoretic Reeb Graphs and Reeb Spaces with Applications.
   
   
9. Invited Talk: BSV Research Seminar on Computer Graphics, Image Processing, and Visualization, November 8, 2023.
   Complex data visualization: climate simulations, high-dimensional point clouds, hypergraphs and beyond.
   
   
10. Invited Talk: Asia Pacific Seminar on Applied Topology and Geometry (APATG), October 27, 2023.
    Hypergraph Co-Optimal Transport: Metric and Categorical Properties.
    
    
11. Workshop: A Hands-on TTK Tutorial for Absolute Beginners at IEEE VIS Conference, October 22, 2023.
    Organizers: Bei Wang, Christoph Garth, Robin Maack, Mathieu Pont, Julien Tierny, Florian Wetzels, Michael Will.

1. Session Chairs, full paper session and Young Researchers Forum at the International Symposium on Computational Geometry (SOCG), June 10-15, 2023.

2. Workshop: Dagstuhl Seminar: Topological Data Analysis and Applications, May 7-12, 2023.
   Organizers: Bei Wang, Ulrich Bauer, Vijay Natarajan.

3. Invited Talk (virtual), Colorado State University Topology Seminar, April 18, 2023.

4. Invited Talk (virtual), Northeastern Topology Seminar, April 11, 2023.

5. Invited Talk, Institute for Mathematical and Statistical Innovation (IMSI), Randomness in Topology and its Applications workshop, March 21, 2023.

6. Keynote Talk, Machine Learning on Higher-Order Structured data (ML-HOS) Workshop at ICDM 2022. Hypergraph Co-Optimal Transport, November 28, 2022.

7. Invited Talk, Stochastic Seminar, Department of Mathematics, University of Utah, November 4, 2022.

8. Workshop: Topological Analysis of Ensemble Scalar Data with TTK, A Sequel at IEEE VIS Conference, October 16-21, 2022.
   Organizers: Bei Wang, Christoph Garth, Charles Gueunet, Pierre Guillou, Federico Iuricich, Joshua A Levine, Jonas Lukasczyk, Mathieu Pont, Julien Tierny, Jules Vidal, Florian Wetzels.

9. Invited Talk, Mini Symposium on Statistics and Machine Learning in Topological and Geometric Data Analysis at SIAM Conference on Mathematics of Data Science (MDS22), September 29, 2022.

Students

Collaborators

Dr. Lin Yan, Environmental Science & Mathematics and Computer Science, Argonne National Laboratory, Lemont, USA

Dr. Paul Aaron Ullrich, Department of Land, Air and Water Resources, University of California, Davis, USA

Dr. Luke P. Van Roekel, Fluid Dynamics and Solid Mechanics, Los Alamos National Laboratory Los Alamos, USA

Dr. Hanqi Guo, Department of Computer Science and Engineering, The Ohio State University, Columbus, USA

Acknowledgement

This material is based upon work supported or partially supported by the National Science Foundation under Grant No. 2145499.

Any opinions, findings, and conclusions or recommendations expressed in this project are those of author(s) and do not necessarily reflect the views of the National Science Foundation.

Web page last update: June 18, 2024.