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Topology-Preserving Data Sketching for Scientific Visualization
FY 2020 DOE Office of Science Early Career Research Program

Award Number and Duration

DOE DE-SC0021015

September 1, 2020 to August 31, 2025 (Estimated)

PI and Point of Contact

Bei Wang Phillips (Publish Under Bei Wang)
Assistant 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

We are experiencing an information overload from streams of data that arise from scientific instruments and simulations. For example, material scientists use molecular dynamics (MD) simulations to study how fluids (such as gas, oil, and water) interact with heterogeneous porous solids (such as ceramics, cement, and rock) to improve transport phenomena within porous materials, which play critical roles in our energy sector. Such simulations generate large, time-varying, and complex forms of data under different physical and chemical conditions. Keeping track of interesting phenomena and applying appropriate actions (such as storage, analysis, and visualization) while the simulation is running is necessary but challenging. To address this challenge, the goal is no longer to capture and store observations or simulation in detail, but rather to process data efficiently and approximately in order to create a summary - a sketch - which allows queries over large volumes of data to be answered quickly.

The objective of this research is to conduct a systematic study of topology-preserving data sketching techniques to improve visual exploration and understanding of large scientific data. The project will employ topological sketches, that is, compressed representations of the full data that preserve their important structural properties, to support analysis and visualization as the data are generated. Our proposed solution transforms data sketching ideas from statistics, geometry, and linear algebra to develop new topological sketches of complex data. Such sketches will exploit the high spatial resolution and temporal fidelity of in situ data in an intelligent and scalable way. They will reduce data in situ while preserving its structural properties, and subsequently support interactive data exploration. In addition, topological triggers will be integrated into an adaptive workflow to support anomaly detection, computational steering, and decision optimization. The multidisciplinary nature of the proposed work will be broadly applicable in many scientific areas, including applications in computational fluid dynamics and materials science.

Publications and Manuscripts

Papers marked with * use alphabetic ordering of authors.
Year 3 (2022 - 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
arXiv:2209.11708


PDF Meta-diagrams for 2-parameter persistence.
Nate Clause, Tamal K. Dey, Facundo Mémoli, Bei Wang*.
International Symposium on Computational Geometry (SOCG), 2023.

PDF Flexible and Probabilistic Topology Tracking with Partial Optimal Transport.
Mingzhe Li, Xinyuan Yan, Lin Yan, Tom Needham, Bei Wang.
Manuscript, 2023.
arXiv:2302.02895.
PDF Hypergraph Co-Optimal Transport: Metric and Categorical Properties.
Samir Chowdhury, Tom Needham, Ethan Semrad, Bei Wang, Youjia Zhou.
Manuscript, 2023.
arXiv:2112.03904.
PDF Sketching and Vectorizing Merge Trees for Scientific Data Visualization.
Mingzhe Li, Sourabh Palande, Lin Yan, Bei Wang.
Manuscript, 2023.
arXiv:2101.03196.
PDF Labeled Interleaving Distance for Reeb Graphs.
Fangfei Lan, Salman Parsa, Bei Wang.
Manuscript, 2023.
arXiv:2306.01186
TROPHY: A Topologically Robust Physics-Informed Tracking Framework for Tropical Cyclone.
Lin Yan, Hanqi Guo, Tom Peterka, Bei Wang, Jiali Wang.
Manuscript, 2023.

Homology-Preserving Multi-scale Graph Skeletonization Using Mapper on Graphs.
Paul Rosen, Mustafa Hajij, Bei Wang.
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 Uncertainty Visualization for Graph Coarsening.
 Fangfei Lan, Sourabh Palande, Michael Young, Bei Wang.
IEEE International Conference on Big Data (IEEE BigData), 2022.
DOI: 10.1109/BigData55660.2022.10021039
PDF Reduced Connectivity for Local Bilinear Jacobi Sets.
Daniel Klötzl, Tim Krake, Youjia Zhou, Jonathan Stober, Kathrin Schulte, Ingrid Hotz, Bei Wang, Daniel Weiskopf.
IEEE Workshop on Topological Data Analysis and Visualization (TopoInVis) at IEEE VIS, 2022.
DOI: 10.1109/TopoInVis57755.2022.00011
arXiv:2208.07148
Honorable Mention Paper Award.
PDF Untangling Force-Directed Layouts Using Persistent Homology.
Bhavana Doppalapudi, Bei Wang, Paul Rosen.
IEEE Workshop on Topological Data Analysis and Visualization (TopoInVis) at IEEE VIS, 2022.
DOI: 10.1109/TopoInVis57755.2022.00015
arXiv:2208.06927

Year 2 (2021 - 2022)
PDF Geometry-Aware Merge Tree Comparisons for Time-Varying Data with Interleaving Distances.
Lin Yan, Talha Bin Masood, Farhan Rasheed, Ingrid Hotz, Bei Wang.
IEEE Transactions on Visualization and Computer Graphics (TVCG), 2022.
DOI: 10.1109/TVCG.2022.3163349 (early access)
arXiv:2107.14373
PDF Topological Simplifications of Hypergraphs.
Youjia Zhou, Archit Rathore, Emilie Purvine, Bei Wang.
IEEE Transactions on Visualization and Computer Graphics (TVCG), 2022.
DOI: 10.1109/TVCG.2022.3153895 (early access)
arXiv:2104.11214.
PDF Local Bilinear Computation of Jacobi Sets
 Daniel Klötzl, Tim Krake, Youjia Zhou, Ingrid Hotz, Bei Wang, Daniel Weiskopf.
Computer Graphics International (CGI), 2022.
Visual Computer, 38, pages 3435-3448, 2022.
DOI: 10.1007/s00371-022-02557-4
Visual Computer Second Best Paper Award.
PDF Stitch Fix for Mapper and Topological Gains.
Youjia Zhou, Nathaniel Saul, Ilkin Safarli, Bala Krishnamoorthy, Bei Wang.
Research in Computational Topology 2, Association for Women in Mathematics Series, vol 30, pages 265-294, Springer, Cham. 2022.
Editors: Ellen Gasparovic, Vanessa Robins, Katharine Turner.
DOI: 10.1007/978-3-030-95519-9_12
PDF Graph Pseudometrics from a Topological Point of View.
Ana Lucia Garcia-Pulido, Kathryn Hess, Jane Tan, Katharine Turner, Bei Wang, Naya Yerolemou.
Research in Computational Topology 2, Association for Women in Mathematics Series, vol 30, pages 99-128, Springer, Cham. 2022.
Editors: Ellen Gasparovic, Vanessa Robins, Katharine Turner.
DOI: 10.1007/978-3-030-95519-9_5

Year 1 (2020 - 2021)
PDF Scalar Field Comparison with Topological Descriptors: Properties and Applications for Scientific Visualization.
Lin Yan, Talha Bin Masood, Raghavendra Sridharamurthy, Farhan Rasheed, Vijay Natarajan, Ingrid Hotz, Bei Wang.
Eurographics Conference on Visualization (EuroVis), 2021.
Computer Graphics Forum, 40(3), pages 599-633, 2021.
DOI: 10.1111/cgf.14331

Software Downloads

Topological Simplification of Hypergraphs
https://github.com/tdavislab/Hypergraph-Vis

 An interactive toolbox for interactive visualization of hypergraphs and their simplifications.

Presentations, Educational Development and Broader Impacts

Year 3 (2022 - 2023)

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

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

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

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

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

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

  7. Bei Wang Invited Talk, Dagstuhl Seminar on Set Visualization and Uncertainty, Germany. Visualizing Hypergraphs With Connections to Uncertainty Visualization. November 13-18, 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.

Year 2 (2021 - 2022)

  1. Bei Wang Invited Talk (virtual), Applied, Combinatorial and Toric Topology at Institute for Mathematical Sciences, Singapore, July, 2022.

  2. Workshop: Topological Data Visualization Workshop at University of Iowa, May 16 - 20, 2022.
    Organizers: Bei Wang, Isabel K. Darcy.

  3. Bei Wang Invited Talk (virtual), Spring Western AMS Sectional Meeting, May, 2022.

  4. Bei Wang Invited Talk (virtual), Mathematical Biology Seminar at the Department of Mathematics, University of Iowa, May, 2022.

  5. Bei Wang Invited Talk (virtual), Women in Data Science (WiDS) Ames Regional Event at Iowa State University, April, 2022.

  6. Bei Wang Invited Talk (virtual), Colloquium Talk at Department of Computational Mathematics, Science, and Engineering (CMSE), Michigan State University, April, 2022.

  7. Bei Wang Two Invited Talks (virtual), Joint Mathematics Meetings, April, 2022

  8. Bei Wang Contributed Talk (virtual), Visualization Seminar, University of Utah, March, 2022.

  9. Bei Wang Invited Talk (virtual), Workshop on Algebraic Combinatorics and Category Theory in Topological Data Analysis, March, 2022.

  10. Bei Wang Invited Talk (virtual), IMSI workshop on Mathematics of Soft Matter, March, 2022.

  11. Bei Wang Invited Talk (virtual), TDA Week, Japan, February, 2022.

  12. Bei Wang Invited Talk (virtual), SIAM Pacific Northwest (PNW) Distinguished Seminar, February, 2022

  13. Bei Wang Invited Talk (virtual), Computational Persistence Workshop, November, 2021.

  14. Bei Wang Invited Talk (virtual), Seminar GEOTOP-A: Applications of geometry and topology, August, 2021.
Year 1 (2020 - 2021)

  1. Workshop: Topological Analysis of Ensemble Scalar Data with TTK at IEEE VIS, October 24-29, 2021.
    Organizers: Bei Wang, Christoph Garth, Charles Gueunet, Pierre Guillou, Lutz Hofmann, Joshua A Levine, Jonas Lukasczyk, Julien Tierny, Jules Vidal, Florian Wetzels.

  2. Bei Wang Invited Talk (virtual), ILJU Pohang University of Science Technology (POSTECH) Mathematical Institute for Data Science (MINDS) Workshop on Topological Data Analysis and Machine Learning, South Korea, July, 2021.

  3. Bei Wang Invited Talk (virtual), SIAM Conference on Applications of Dynamical Systems (DS21), Mini-symposium on Topological Signal Processing, May 2021.

  4. Bei Wang Invited Talk (virtual), MSRI (Mathematical Sciences Research Institute) Hot Topics: Topological Insights In Neuroscience, May 2021.

  5. Bei Wang Invited Talk (virtual), Applied Algebraic Topology Research Network (AATRN) Vietoris-Rips Seminar, May 2021.

  6. Bei Wang Invited Talk (virtual), Geometry-Topology Seminar, Oregon State University, May, 2021.

  7. Bei Wang Invited Talk (virtual), Computational Mathematics, Science and Engineering (CMSE) Colloquiums, Michigan State University, April, 2021.

  8. Bei Wang Invited Talk (virtual), Meldrum Science Seminar Series, Westminster College, April, 2021.

  9. Bei Wang Contributed Talk (virtual) at IMSI workshop on Topological Data Analysis, Institute for Mathematical and Statistical Innovation, April, 2021.

  10. Bei Wang Invited Talk (virtual) at CAM Colloquium, Committee on Computational and Applied Mathematics (CCAM), University of Chicago, March, 2021.

  11. Workshop: Application Spotlights: Challenges in the Visualization of Bioelectric Fields for Cardiac and Neural Research at IEEE VIS, October 25-30, 2020.
    Organizers: Bei Wang, Rob MacLeod, Wilson Good.

Postdoc and Students

Mingzhe Li (Ph.D. student)
School of Computing and Scientific Computing and Imaging Institute
University of Utah

Fangfei Lan (Ph.D. student)
School of Computing and Scientific Computing and Imaging Institute
University of Utah

Dr. Raghavendra Sridharamurthy (Postdoc, April 2023 - present)
School of Computing and Scientific Computing and Imaging Institute
University of Utah

Dr. Salman Parsa (Postdc, January 2022 - August 2022)
Scientific Computing and Imaging Institute
University of Utah

Collaborators

Dr. Pania Newell, Assistant Professor, Department of Mechanical Engineering; University of Utah.

Dr. Anastasia Ilgen, Sandia National Lab.

Dr. Roxana Bujack, Los Alamos National Laboratory.

Dr. Emilie Purvine, Pacific Northwest National Laboratory.

Dr. Gunther Weber, Lawrence Berkeley National Laboratory.

Acknowledgement

This material is based upon work supported or partially supported by the United States Department of Energy (DOE) under Grant No. DE-SC0021015.

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 DOE.

Web page last update: May 31, 2023.