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


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

Year 1 (2022 - 2023)

PDF Meta-diagrams for 2-parameter persistence.
Nate Clause, Tamal K. Dey, Facundo Mémoli, Bei Wang.
International Symposium on Computational Geometry (SOCG), 2023.
PDF TopoSZ: Preserving Topology in Error-Bounded Lossy Compression.
Lin Yan, Xin Liang, Hanqi Guo, Bei Wang.
IEEE Visualization Conference, conditional accepted, 2023.
TROPHY: A Topologically Robust Physics-Informed Tracking Framework for Tropical Cyclone.
Lin Yan, Hanqi Guo, Tom Peterka, Bei Wang, Jiali Wang.
IEEE Visualization Conference, conditional accepted, 2023.

PDF Flexible and Probabilistic Topology Tracking with Partial Optimal Transport.
Mingzhe Li, Xinyuan Yan, Lin Yan, Tom Needham, Bei Wang.
Manuscript, 2023.
PDF Hypergraph Co-Optimal Transport: Metric and Categorical Properties.
Samir Chowdhury, Tom Needham, Ethan Semrad, Bei Wang, Youjia Zhou.
Manuscript, 2023.
Comparing Morse Complexes Using Optimal Transport: An Experimental Study.
Carson Storm, Mingzhe Li, Austin Yang Li, Tom Needham, Bei Wang.
Manuscript, 2023.

PDF Labeled Interleaving Distance for Reeb Graphs.
Fangfei Lan, Salman Parsa, Bei Wang.
Manuscript, 2023.
PDF Sketching and Vectorizing Merge Trees for Scientific Data Visualization.
Mingzhe Li, Sourabh Palande, Lin Yan, Bei Wang.
Manuscript, 2023.

PDF Multilevel Robustness for 2D Vector Field Feature Tracking, Selection, and Comparison.
Lin Yan, Paul Aaron Ullrich, Luke P. Van Roekel, Bei Wang, Hanqi Guo.
Computer Graphics Forum, 2023.
DOI: 10.1111/cgf.14799

PDF Uncertainty Visualization for Graph Coarsening.
Fangfei Lan, Sourabh Palande, Michael Young, Bei Wang.
IEEE International Conference on Big Data (IEEE BigData), pages 2922-2931, 2022.
DOI: 10.1109/BigData55660.2022.10021039

Presentations, Educational Development and Broader Impacts

Year 1 (2022 - 2023)
  1. Bei Wang Keynote Talk (upcoming), TDA Week, Japan, July 21 - August 4, 2023.

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

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

  4. Bei Wang Invited Talk (virtual), Colorado State University Topology Seminar, April 18, 2023.

  5. Bei Wang Invited Talk (virtual), Northeastern Topology Seminar, April 11, 2023.

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

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

  8. Bei Wang Invited Talk, Stochastic Seminar, Department of Mathematics, University of Utah, November 4, 2022.

  9. 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.

  10. Bei Wang 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.


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


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 7, 2023.