Bei Wang

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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 5 (2024 - 2025)
	Tracking Low-Level Cloud Systems with Topology. Mingzhe Li, Dwaipayan Chatterjee, Franziska Glassmeier, Fabian Senf, Bei Wang. Manuscript, 2025.
	Measure-Theoretic Reeb Graphs and Reeb Spaces. Qingsong Wang, Guanqun Ma, Raghavendra Sridharamurthy, Bei Wang. Discrete & Computational Geometry (DCG), minor revision, 2025. arXiv:2401.06748.
	Meta-diagrams for 2-parameter persistence. Nate Clause, Tamal K. Dey, Facundo Mémoli, Bei Wang. Discrete & Computational Geometry (DCG), accepted, 2025.
	Finding the Cores of Higher Graphs Using Geometric and Topological Means: A Survey. Inés García-Redondo, Claudia Landi, Sarah Percival, Anda Skeja, Bei Wang, Ling Zhou. Research in Computational Topology 3, Association for Women in Mathematics Series, Springer, Cham, accepted, 2025.
	Tracking the Persistence of Harmonic Chains: Barcode and Stability. Tao Hou, Salman Parsa, Bei Wang. International Symposium on Computational Geometry (SOCG), 2025. arXiv:2412.15419.
	Flexible and Probabilistic Topology Tracking with Partial Optimal Transport. Mingzhe Li, Xinyuan Yan, Lin Yan, Tom Needham, Bei Wang. IEEE Transactions on Visualization and Computer Graphics, 2025. DOI: 10.1109/TVCG.2025.3561300 arXiv:2302.02895.
	Distributed Augmentation, Hypersweeps, and Branch Decomposition of Contour Trees for Scientific Exploration. Mingzhe Li, Hamish Carr, Oliver Rubel, Bei Wang, Gunther H. Weber. IEEE Visualization Conference (IEEE VIS), 2024. IEEE Transactions on Visualization and Computer Graphics, 31(1), pages 152-162, 2025. DOI:10.1109/TVCG.2024.3456322 arXiv:2408.04836
	Fast Comparative Analysis of Merge Trees Using Locality-Sensitive Hashing. Weiran Lyu, Raghavendra Sridharamurthy, Jeff M. Phillips, Bei Wang. IEEE Visualization Conference (IEEE VIS), 2024. IEEE Transactions on Visualization and Computer Graphics, 31(1), pages 141-151, 2025. DOI:10.1109/TVCG.2024.3456383 arXiv:2409.08519
	MSz: An Efficient Parallel Algorithm for Correcting Morse-Smale Segmentations in Error-Bounded Lossy Compressors. Yuxiao Li, Xin Liang, Bei Wang, Yongfeng Qiu, Lin Yan, Hanqi Guo. IEEE Visualization Conference (IEEE VIS), 2024. IEEE Transactions on Visualization and Computer Graphics, 31(1), pages 130-140, 2025. DOI:10.1109/TVCG.2024.3456337 Supplement 1. Supplement 2: Detailed figures from Figure 7 and Figure 8 in the main paper. arXiv:2406.09423
	A Survey of Simplicial, Relative, and Chain Complex Homology Theories for Hypergraphs. Ellen Gasparovic, Emilie Purvine, Radmila Sazdanovic, Bei Wang, Yusu Wang, Lori Ziegelmeier. Manuscript, 2024. arXiv:2409.18310
	Geometry of the Space of Partitioned Networks: A Unified Theoretical and Computational Framework. Stephen Y Zhang, Fangfei Lan, Youjia Zhou, Agnese Barbensi, Michael P H Stumpf, Bei Wang, Tom Needham. Manuscript, 2024. arXiv:2409.06302
	EulerMerge: Simplifying Euler Diagrams Through Set Merges. Xinyuan Yan, Peter Rodgers, Peter Rottmann, Daniel Archambault, Jan-Henrik Haunert, Bei Wang. Proceedings of the 14th International Conference on the Theory and Application of Diagrams (DIAGRAMS), 2024. DOI:10.1007/978-3-031-71291-3_16
	Labeled Interleaving Distance for Reeb Graphs. Fangfei Lan, Salman Parsa, Bei Wang. Journal of Applied and Computational Topology, 8, pages 2367-2399, 2024. DOI:10.1007/s41468-024-00193-6 arXiv:2306.01186
Year 4 (2023 - 2024)
	Topological Characterization and Uncertainty Visualization of Atmospheric Rivers. Fangfei Lan, Brandi Gamelin, Lin Yan, Jiali Wang, Bei Wang, Hanqi Guo. Eurographics Conference on Visualization (EuroVis), 2024. Computer Graphics Forum, 43(3), e15084, 2024. DOI:10.1111/cgf.15084
	Generating Euler Diagrams Through Combinatorial Optimization. Peter Rottmann, Peter Rodgers, Xinyuan Yan, Daniel Archambault, Bei Wang, Jan-Henrik Haunert. Eurographics Conference on Visualization (EuroVis), 2024. Computer Graphics Forum, 43(3), e15089, 2024. DOI:10.1111/cgf.15089
	Labeled Interleaving Distance for Reeb Graphs (Abstract). Fangfei Lan, Salman Parsa, Bei Wang. International Symposium on Computational Geometry (SOCG) Young Researcher Forum (YRF), 2024.
	Measure-Theoretic Reeb Graphs and Reeb Spaces. Qingsong Wang, Guanqun Ma, Raghavendra Sridharamurthy, Bei Wang. International Symposium on Computational Geometry (SOCG), 2024. DOI:10.4230/LIPIcs.SoCG.2024.80 arXiv:2401.06748.
	TopoSZ: Preserving Topology in Error-Bounded Lossy Compression. Lin Yan, Xin Liang, Hanqi Guo, Bei Wang. IEEE Visualization Conference (IEEE VIS), 2023. IEEE Transactions on Visualization and Computer Graphics (TVCG), 30, pages 1302-1312, 2024. Supplementary Material. DOI:10.1109/TVCG.2023.3326920 arXiv:2304.11768.
	TROPHY: A Topologically Robust Physics-Informed Tracking Framework for Tropical Cyclone. Lin Yan, Hanqi Guo, Tom Peterka, Bei Wang, Jiali Wang. IEEE Visualization Conference (IEEE VIS), 2023. IEEE Transactions on Visualization and Computer Graphics (TVCG), 30, pages 1249-1259, 2024. Supplementary Material. DOI:10.1109/TVCG.2023.3326905 arXiv:2307.15243.
	Comparing Morse Complexes Using Optimal Transport: An Experimental Study. Mingzhe Li, Carson Storm, Austin Yang Li, Tom Needham, Bei Wang. IEEE Visualization and Visual Analytics (VIS) Short Paper, pages 41-45, 2023. Supplementary Material. DOI:10.1109/VIS54172.2023.00017
	Sketching Merge Trees for Scientific Visualization. Mingzhe Li, Sourabh Palande, Lin Yan, Bei Wang. IEEE Workshop on Topological Data Analysis and Visualization (TopoInVis) at IEEE VIS, pages 61-71, 2023. Supplementary Material. DOI:10.1109/TopoInVis60193.2023.00013 arXiv:2101.03196.
	Homology-Preserving Multi-Scale Graph Skeletonization Using Mapper on Graphs. Mustafa Hajij, Bei Wang, Paul Rosen. IEEE Workshop on Topological Data Analysis and Visualization (TopoInVis) at IEEE VIS, pages 10-20, 2023. Supplementary Material: User study data. DOI:10.1109/TopoInVis60193.2023.00008 arXiv:1804.11242.
	Combinatorial Exploration of Morse-Smale Functions on the Sphere via Interactive Visualization. Youjia Zhou, Janis Lazovskis, Michael J. Catanzaro, Matthew Zabka, Bei Wang. IEEE Workshop on Topological Data Analysis and Visualization (TopoInVis) at IEEE VIS, pages 51-60, 2023. DOI:10.1109/TopoInVis60193.2023.00012 arXiv:1912.09580.
	Hypergraph Co-Optimal Transport: Metric and Categorical Properties. Samir Chowdhury, Tom Needham, Ethan Semrad, Bei Wang, Youjia Zhou. Journal of Applied and Computational Topology, 2023. DOI:10.1007/s41468-023-00142-9 arXiv:2112.03904
Year 3 (2022 - 2023)
	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, 42(6), e14799, 2023. DOI: 10.1111/cgf.14799 arXiv:2209.11708
	Meta-diagrams for 2-parameter persistence. Nate Clause, Tamal K. Dey, Facundo Mémoli, Bei Wang. International Symposium on Computational Geometry (SOCG)*, 2023. DOI:10.4230/LIPIcs.SoCG.2023.25
	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
	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.
	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)
	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), 29(8), pages 3489-3506, 2023. DOI: 10.1109/TVCG.2022.3163349 arXiv:2107.14373
	Topological Simplifications of Hypergraphs. Youjia Zhou, Archit Rathore, Emilie Purvine, Bei Wang. IEEE Transactions on Visualization and Computer Graphics (TVCG), 29(7), pages 3209-3225, 2023. DOI: 10.1109/TVCG.2022.3153895 arXiv:2104.11214.
	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.
	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
	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)
	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 4 (2023 - 2024)

Invited Talk: Department of Computer Science, Aarhus University, May 31, 2024.
Capturing Robust Topology in Data.
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.
Invited Talk: Data Science and Applied Topology Seminar at the City University of New York, April 5, 2024.
Reeb Graphs and Measure Theoretic Variants.
Overview Talk: Dagstuhl Seminar 24092: Applied and Combinatorial Topology, Dagstuhl, Germany, Feb 26, 2024.
Reeb Graphs and Their Variants: Theory and Application.
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.
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.
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.
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.
Invited Talk: Asia Pacific Seminar on Applied Topology and Geometry (APATG), October 27, 2023.
Hypergraph Co-Optimal Transport: Metric and Categorical Properties.
Invited Talk: Computational Oncology Research Initiative (CORI) Speaker Series, October 23, 2023.
Visualizing Metabolic Networks and Beyond.
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.
Invited Talk: School of Physical and Mathematical Sciences, Nanyang Technological University, October 19, 2023.
Topology of Artificial Neuron Activations in Deep Learning.

Year 3 (2022 - 2023)

Invited Talk: Dagstuhl Seminar on Computational Geometry of Earth System Analysis, August 21, 2023.
Topological Characterization and Uncertainty Visualization of Atmospheric Rivers.
Invited Talk: International Forum at the China Visualization and Visual Analytics Conference (ChinaVis), July 21, 2023.
Workshop: Dagstuhl Seminar: Topological Data Analysis and Applications, May 7-12, 2023.
Organizers: Bei Wang, Ulrich Bauer, Vijay Natarajan.
Invited Talk (virtual), Colorado State University Topology Seminar, April 18, 2023.
Invited Talk (virtual), Northeastern Topology Seminar, April 11, 2023.
Invited Talk, Institute for Mathematical and Statistical Innovation (IMSI), Randomness in Topology and its Applications workshop, March 21, 2023.
Keynote Talk, Machine Learning on Higher-Order Structured data (ML-HOS) Workshop at ICDM 2022. Hypergraph Co-Optimal Transport, November 28, 2022.
Invited Talk, Dagstuhl Seminar on Set Visualization and Uncertainty, Germany. Visualizing Hypergraphs With Connections to Uncertainty Visualization. November 13-18, 2022.
Invited Talk, Stochastic Seminar, Department of Mathematics, University of Utah, November 4, 2022.
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.
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)

Invited Talk (virtual), Applied, Combinatorial and Toric Topology at Institute for Mathematical Sciences, Singapore, July, 2022.
Workshop: Topological Data Visualization Workshop at University of Iowa, May 16 - 20, 2022.
Organizers: Bei Wang, Isabel K. Darcy.
Invited Talk (virtual), Spring Western AMS Sectional Meeting, May, 2022.
Invited Talk (virtual), Mathematical Biology Seminar at the Department of Mathematics, University of Iowa, May, 2022.
Invited Talk (virtual), Women in Data Science (WiDS) Ames Regional Event at Iowa State University, April, 2022.
Invited Talk (virtual), Colloquium Talk at Department of Computational Mathematics, Science, and Engineering (CMSE), Michigan State University, April, 2022.
Two Invited Talks (virtual), Joint Mathematics Meetings, April, 2022
Contributed Talk (virtual), Visualization Seminar, University of Utah, March, 2022.
Invited Talk (virtual), Workshop on Algebraic Combinatorics and Category Theory in Topological Data Analysis, March, 2022.
Invited Talk (virtual), IMSI workshop on Mathematics of Soft Matter, March, 2022.
Invited Talk (virtual), TDA Week, Japan, February, 2022.
Invited Talk (virtual), SIAM Pacific Northwest (PNW) Distinguished Seminar, February, 2022
Invited Talk (virtual), Computational Persistence Workshop, November, 2021.
Invited Talk (virtual), Seminar GEOTOP-A: Applications of geometry and topology, August, 2021.

Year 1 (2020 - 2021)

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.
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.
Invited Talk (virtual), SIAM Conference on Applications of Dynamical Systems (DS21), Mini-symposium on Topological Signal Processing, May 2021.
Invited Talk (virtual), MSRI (Mathematical Sciences Research Institute) Hot Topics: Topological Insights In Neuroscience, May 2021.
Invited Talk (virtual), Applied Algebraic Topology Research Network (AATRN) Vietoris-Rips Seminar, May 2021.
Invited Talk (virtual), Geometry-Topology Seminar, Oregon State University, May, 2021.
Invited Talk (virtual), Computational Mathematics, Science and Engineering (CMSE) Colloquiums, Michigan State University, April, 2021.
Invited Talk (virtual), Meldrum Science Seminar Series, Westminster College, April, 2021.
Contributed Talk (virtual) at IMSI workshop on Topological Data Analysis, Institute for Mathematical and Statistical Innovation, April, 2021.
Invited Talk (virtual) at CAM Colloquium, Committee on Computational and Applied Mathematics (CCAM), University of Chicago, March, 2021.
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 - March 2024)
School of Computing and Scientific Computing and Imaging Institute
University of Utah

Dr. Salman Parsa (Postdoc, 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 2, 2025.