# META: Multifield Extension of Topological Analysis

Lead Research Organisation:
University of Leeds

Department Name: Sch of Computing

### Abstract

Physical scientists, engineers and clinicians rely on visualization to obtain insight into data arising from scans and simulation. Since the 1980s, when an influential US NSF report ushered in the use of graphics to make sense of large volumes of numerical data, visualization techniques have advanced in surges marked by major breakthroughs, including: "marching cubes" and its derivatives for interpreting scalar fields, volume rendering for inherently volumetric data; and vector field topology for understanding the structure of flow. However, existing visualization techniques are limited to individual properties of data, temperature, pressure, velocity, vorticity, shear, combustion rate, rainfall, and so on.

Techniques for multivariate (multifield) data do exist in information visualization, where parallel coordinates, spider plots etc are widely used. But these tools are of little use for scientific datasets, where the interpretation of data is intimately tied to physical space/time, or to the scale of scientific datasets, which is routinely measured in gigabytes or terabytes. The key problem is that, until now, we have lacked any suitable mathematical and computational model for multifield analysis. The mathematics is needed to explain what exactly it means to understand how multiple fields interact; the computational model is needed to explain how this interaction can be mapped into visual representations that can be generated efficiently from large volumes of data. Techniques for multifield analysis would be of enormous benefit right across the diverse range of application domains that rely on (scientific) visualization, including aerospace, materials engineering, climatology and meterology, astrophysics, radiology and surgical planning. It would enable new scientific insight, and provide industry with new tools through which to develop competitive advantage.

Recent work by the applicants has achieved a breakthrough result. The "Joint Contour Net" is a new abstraction that hold great promise in providing the mathematical and computational machinery needed for multifields. The origins of the JCN are in computational topology, a field that, over the last decade, has made major contributions to visualization through finding and explaining structure within data. Topology provides a rigorous foundation for identifying features and transitions within data, and these are of particular interest to end users in understanding the original problem. Topological models are also essential in simplifying and presenting massive datasets, as our ability to interpret data has to pass through the bottleneck of screen space (typically around 2M pixels) and the gigabyte limits of the human visual system. The Joint Contour Net provides a first glimpse of how to generalise topological analysis from one field to many fields, and importantly, how to do so efficiently, and in a way that accommodates parallelisation to scale up to processing massive datasets.

This proposal will deliver on the initial promise by developing the mathematical theory for multifield analysis, generating the and the visual abstractions needed to understand multifield behaviour. To achieve this, we will work closely with other international leaders in visualization and computational topology to address specific issues, such as simplification and rendering techniques based on JCNs, and user interfaces for steering analysis that are adapted to the needs of particular applications. To ensure the research has the maximum possible reach, we will embed our software into the most widely used visualization toolkits, with dedicated effort to ensure that the implementation is robust and maintainable, and courses to train end-users in its application.

Techniques for multivariate (multifield) data do exist in information visualization, where parallel coordinates, spider plots etc are widely used. But these tools are of little use for scientific datasets, where the interpretation of data is intimately tied to physical space/time, or to the scale of scientific datasets, which is routinely measured in gigabytes or terabytes. The key problem is that, until now, we have lacked any suitable mathematical and computational model for multifield analysis. The mathematics is needed to explain what exactly it means to understand how multiple fields interact; the computational model is needed to explain how this interaction can be mapped into visual representations that can be generated efficiently from large volumes of data. Techniques for multifield analysis would be of enormous benefit right across the diverse range of application domains that rely on (scientific) visualization, including aerospace, materials engineering, climatology and meterology, astrophysics, radiology and surgical planning. It would enable new scientific insight, and provide industry with new tools through which to develop competitive advantage.

Recent work by the applicants has achieved a breakthrough result. The "Joint Contour Net" is a new abstraction that hold great promise in providing the mathematical and computational machinery needed for multifields. The origins of the JCN are in computational topology, a field that, over the last decade, has made major contributions to visualization through finding and explaining structure within data. Topology provides a rigorous foundation for identifying features and transitions within data, and these are of particular interest to end users in understanding the original problem. Topological models are also essential in simplifying and presenting massive datasets, as our ability to interpret data has to pass through the bottleneck of screen space (typically around 2M pixels) and the gigabyte limits of the human visual system. The Joint Contour Net provides a first glimpse of how to generalise topological analysis from one field to many fields, and importantly, how to do so efficiently, and in a way that accommodates parallelisation to scale up to processing massive datasets.

This proposal will deliver on the initial promise by developing the mathematical theory for multifield analysis, generating the and the visual abstractions needed to understand multifield behaviour. To achieve this, we will work closely with other international leaders in visualization and computational topology to address specific issues, such as simplification and rendering techniques based on JCNs, and user interfaces for steering analysis that are adapted to the needs of particular applications. To ensure the research has the maximum possible reach, we will embed our software into the most widely used visualization toolkits, with dedicated effort to ensure that the implementation is robust and maintainable, and courses to train end-users in its application.

### Planned Impact

The proposed work will deliver a new technology for understanding data in the physical sciences, engineering and medicine. It will, finally, address a major shortcoming in visualization techniques, the limited tools available for analysing multiple fields of data. Such fields arise routinely in nearly every area where visualization is applied, for example:

* aerospace: interaction between pressure, temperature and vorticity of flows over airfoils and within turbine engines;

* material science:

* combustion studies: temperature, combustible material, and the density of by-products generated

* astrophysics: sky surveys typically acquire data across 50+ sensory channels

* climatology and meteorology: temperature, humidity, rainfall, gaseous species

* radiology and biomedical research: relationships between scanner modalities

* clinical medicine, for example surgical planning:

The impact of the research is therefore both broad and indirect; visualization tools are the "user interface" through which raw data from simulations and scanners is converted into insight. It is this insight that represents the ultimate value of the research, whether it be through basic scientific discovery, improved products such as aircraft engines or materials that give UK companies a competitive edge, or longer-term societal benefit resulting, for example, from: high-value manufacturing (improved engine design); better medical diagnosis, treatment and outcomes through the ability to resolve finer levels of detail and structure in radiological data; new insight into performance of low-carbon energy sources.

The project proposal has specific actions to deliver this impact:

* collaboration with leading international researchers who themselves work directly with industrial applications and research end-users;

* collaboration with the developers of the leading tools for scientific data visualization;

* ring-fenced effort for delivering robust software products into leading visualization packages;

* outreach programme of tutorials targeting three of the broader end-user communities;

* focused CPD training directed at UK end-users from industry and research laboratories.

* aerospace: interaction between pressure, temperature and vorticity of flows over airfoils and within turbine engines;

* material science:

* combustion studies: temperature, combustible material, and the density of by-products generated

* astrophysics: sky surveys typically acquire data across 50+ sensory channels

* climatology and meteorology: temperature, humidity, rainfall, gaseous species

* radiology and biomedical research: relationships between scanner modalities

* clinical medicine, for example surgical planning:

The impact of the research is therefore both broad and indirect; visualization tools are the "user interface" through which raw data from simulations and scanners is converted into insight. It is this insight that represents the ultimate value of the research, whether it be through basic scientific discovery, improved products such as aircraft engines or materials that give UK companies a competitive edge, or longer-term societal benefit resulting, for example, from: high-value manufacturing (improved engine design); better medical diagnosis, treatment and outcomes through the ability to resolve finer levels of detail and structure in radiological data; new insight into performance of low-carbon energy sources.

The project proposal has specific actions to deliver this impact:

* collaboration with leading international researchers who themselves work directly with industrial applications and research end-users;

* collaboration with the developers of the leading tools for scientific data visualization;

* ring-fenced effort for delivering robust software products into leading visualization packages;

* outreach programme of tutorials targeting three of the broader end-user communities;

* focused CPD training directed at UK end-users from industry and research laboratories.

### Organisations

- University of Leeds, United Kingdom (Lead Research Organisation)
- Technical University Kaiserslautern (Collaboration)
- University of Aizu (Collaboration)
- Los Alamos National Laboratory, United States (Collaboration)
- Swiss National Supercomputer Centre (CSCS) (Collaboration)
- Lawrence Livermore National Laboratory, United States (Collaboration)
- Kyushu University, Japan (Collaboration)
- University of Paris 6, France (Collaboration)
- Lawrence Berkeley National Laboratory, United States (Collaboration)
- University of Utah, United States (Collaboration)

## People |
## ORCID iD |

Hamish Carr (Principal Investigator) | |

David Duke (Co-Investigator) |

### Publications

Carr H
(2019)

*Scalable Contour Tree Computation by Data Parallel Peak Pruning.*in IEEE transactions on visualization and computer graphics
Carr H
(2014)

*Joint Contour Nets.*in IEEE transactions on visualization and computer graphics
Carr H
(2015)

*Hybrid data-parallel contour tree computation*
Carr H
(2014)

*Scientific Visualization*
Carr H
(2015)

*Fiber Surfaces: Generalizing Isosurfaces to Bivariate Data*in Computer Graphics Forum
Carr HA
(2016)

*Hybrid data-parallel contour tree computation,*
Chattopadhyay A
(2016)

*Multivariate topology simplification*in Computational Geometry
Dean Thomas
(2017)

*Joint Contour Net Analysis of Lattice QCD Data*
Duke D
(2012)

*Visualizing Nuclear Scission through a Multifield Extension of Topological Analysis.*in IEEE transactions on visualization and computer graphicsDescription | How to generalise from topological analysis of scalar (single-value) data to multivariate (multi-value) data in a computational setting, including computation of analytic structures, identification of features, hierarchical simplification to reduce minor features and noise, mapping to physical phenomena, and integration with existing mathematics of fiber topology. Initial work was also supported on development of faster more scalable algorithms for existing methods. An additional, unanticipated outcome was the discovery of the first geometric solution to visualising local variable relationships in spatial data. |

Exploitation Route | By further development of the existing findings to six- and seven- dimensional cases representing time-varying volumetric data, and to higher-dimensional parameter spaces. By development of application-specific tests for particular domain tasks. Further development on scalability is necessary, and the impact of new visualisation techniques on bivariate data must be explored. |

Sectors | Aerospace, Defence and Marine,Energy,Environment |

URL | http://www.engineering.leeds.ac.uk/computing/research/cse/meta/ |

Description | For analysis of nuclear scission, aiding in determining the transition between single and multiple nuclei, and triggering further developments in the understanding of the process of fission. For analysis of oceanographic data, exploring and understanding movement of cold saline water. For supporting the development of mathematical understanding of fiber topology. For analysis of time-varying radiological drift after Fukushima. For analysis of large-scale combustion simulations For analysis of chemical relationships. Indirectly, has led to other researchers' work on understanding higher-dimensional data. Has also led to analysis of chemical waste leakage through subsoil environments. |

First Year Of Impact | 2014 |

Sector | Chemicals,Construction,Energy,Environment |

Impact Types | Societal |

Description | ECP Alpine/ZFP |

Amount | $12,800,000 (USD) |

Organisation | U.S. Department of Energy |

Sector | Public |

Country | United States |

Start | 04/2019 |

End | 09/2023 |

Description | Collaboration - Kaiserslautern |

Organisation | Technical University Kaiserslautern |

Country | Germany |

Sector | Academic/University |

PI Contribution | Collaboration with colleagues at Technical University of Kaiserslautern. One paper already resulted. |

Collaborator Contribution | Collaborative Research |

Impact | Hüttenberger L, Heine C, Carr H, Scheuermann G, Garth C, Towards Multifield Scalar Topology Based on Pareto Optimality, Computer Graphics Forum 32(3): 341-50, 2013. Garth C, Hüttenberger L, Heine C, Carr H, Scheuermann G, Multivariate Topological Features in Flow Visualization, Workshop on the Analysis of Large-Scale, High-dimensional and Multivariate data Using Topology and Statistics (Le Barp, France, June 12-14, 2013). |

Start Year | 2013 |

Description | Collaboration - Lawrence Livermore |

Organisation | Lawrence Livermore National Laboratory |

Country | United States |

Sector | Public |

PI Contribution | Collaboration with physicist at Lawrence Livermore. Collaboration with nuclear physicists on visualising nuclear scission. Other collaborators located at Argonne National Laboratory, Oak Ridge National Laboratory, and University Marie Curie-Sklodowska, Poland. One paper in Visualization already published. Two papers in physics in preparation to date. |

Collaborator Contribution | Application scientists at Livermore & elsewhere provided data & problem to study |

Impact | Schunck N, Duke DJ, Carr H, Knoll A, Description of induced nuclear fission with Skyrme energy functionals II: II. Finite temperature effects, Physical Review C 91.3: 034527 (2015). Schunck N, Duke DJ, Carr H, Knoll A, Description of induced nuclear fission with Skyrme energy functionals. I. Static potential energy surfaces and fission fragment properties, Physical Review C 90.5: 054305 (2014). Duke D, Carr H, Knoll A, Schunck N, Nam HA, Staszczak A, Visualizing Nuclear Scission Through a Multifield Extension of Topological Analysis, IEEE Transactions on Visualization and Computer Graphics, 18(12): 2033-40, 2012. |

Start Year | 2012 |

Description | Collaboration - Los Alamos National Laboratory |

Organisation | Lawrence Berkeley National Laboratory |

Country | United States |

Sector | Public |

PI Contribution | Massively Parallel Algorithms for Computational Topology. Now part of the US Exascale Computing Project ECP-Alpine. |

Collaborator Contribution | Expertise in massively parallel algorithm development: datasets and systems for large-scale performance tests. |

Impact | H. Carr, C. Sewell, L.-T. Lo, and J. Ahrens. Hybrid data-parallel contour tree computation. Technical Report LA-UR-15-24579, Los Alamos National Laboratory, 2015. Carr H, Sewell C, Lo LT, Ahrens J. Hybrid data-parallel contour tree computation, Computer Graphics & Visual Computing 2016. Carr H, Weber G, Sewell C, Ahrens J, Parallel Peak Pruning for Scalable SMP Contour Tree Computation, Best Paper, IEEE Large Data Analysis & Visualization (LDAV 2016). Contribution of filters to vtk-m toolkit |

Start Year | 2015 |

Description | Collaboration - Los Alamos National Laboratory |

Organisation | Los Alamos National Laboratory |

Department | Data Science at Scale |

Country | United States |

Sector | Public |

PI Contribution | Massively Parallel Algorithms for Computational Topology. Now part of the US Exascale Computing Project ECP-Alpine. |

Collaborator Contribution | Expertise in massively parallel algorithm development: datasets and systems for large-scale performance tests. |

Impact | H. Carr, C. Sewell, L.-T. Lo, and J. Ahrens. Hybrid data-parallel contour tree computation. Technical Report LA-UR-15-24579, Los Alamos National Laboratory, 2015. Carr H, Sewell C, Lo LT, Ahrens J. Hybrid data-parallel contour tree computation, Computer Graphics & Visual Computing 2016. Carr H, Weber G, Sewell C, Ahrens J, Parallel Peak Pruning for Scalable SMP Contour Tree Computation, Best Paper, IEEE Large Data Analysis & Visualization (LDAV 2016). Contribution of filters to vtk-m toolkit |

Start Year | 2015 |

Description | Collaboration - Paris UPMC 6 & University of Utah |

Organisation | Pierre and Marie Curie University - Paris 6 |

Country | France |

Sector | Academic/University |

PI Contribution | Expertise in topological visualisation |

Collaborator Contribution | Data sets; expertise in visualisation |

Impact | Tierny J, Carr H, Jacobi Fiber Surfaces for Bivariate Reeb Space Computation, 23(1): 960-9 (2017). Best Scientific Visualization Paper (IEEE Vis 2016) Klacansky P, Tierny J, Carr H, Geng Z, Fast and Exact Fiber Surfaces for Tetrahedral Meshes, IEEE Transactions on Visualization and Computer Graphics 99: 1-1 (2016). Wu K, Knoll A, Isaac BJ, Carr H, Pascucci V, Direct Multifield Volume Ray Casting of Fiber Surfaces, 23(1): 941-9 (2017). Carr H, Geng Z, Tierny J, Chattopadhyay A, Knoll A, Fiber Surfaces: Generalizing Isosurfaces to Bivariate Data, Computer Graphics Forum 34(3): 241-250 (2015). Contribution of filters to open-source vtk toolkit |

Start Year | 2014 |

Description | Collaboration - Paris UPMC 6 & University of Utah |

Organisation | University of Utah |

Department | Scientific Computing and Imaging Institute |

Country | United States |

Sector | Academic/University |

PI Contribution | Expertise in topological visualisation |

Collaborator Contribution | Data sets; expertise in visualisation |

Impact | Tierny J, Carr H, Jacobi Fiber Surfaces for Bivariate Reeb Space Computation, 23(1): 960-9 (2017). Best Scientific Visualization Paper (IEEE Vis 2016) Klacansky P, Tierny J, Carr H, Geng Z, Fast and Exact Fiber Surfaces for Tetrahedral Meshes, IEEE Transactions on Visualization and Computer Graphics 99: 1-1 (2016). Wu K, Knoll A, Isaac BJ, Carr H, Pascucci V, Direct Multifield Volume Ray Casting of Fiber Surfaces, 23(1): 941-9 (2017). Carr H, Geng Z, Tierny J, Chattopadhyay A, Knoll A, Fiber Surfaces: Generalizing Isosurfaces to Bivariate Data, Computer Graphics Forum 34(3): 241-250 (2015). Contribution of filters to open-source vtk toolkit |

Start Year | 2014 |

Description | Collaboration - University of Tokyo |

Organisation | Kyushu University |

Country | Japan |

Sector | Academic/University |

PI Contribution | Collaboration with University of Tokyo. Research on the META project led to collaborative visit to groups in Tokyo & Kyushu, reciprocal visit by student: development of collaborative publications has begun. |

Collaborator Contribution | Mathematical expertise & problems. |

Impact | Chattopadhyay A, Carr H, Duke DJ, Geng Z, Saeki O, Multivariate Topology Simplification and Measure Persistence, Computational Geometry: Theory & Algorithms 58:1-24 (2017). Sakurai D, Saeki O, Carr H, Wu, Hsiang-Yun, Yamamoto T, Duke D, Takahashi S, Interactive Visualization for Singular Fibers of Functions f:R3->R2, IEEE VisWeek 2015 (IEEE Transactions on Visualization and Computer Graphics 22(1): 945-954 (2016)). Saeki O, Takahashi S, Sakurai D, Wu H-Y, Kikuchi K, Carr H, Duke D, Visualizing Multivariate Data Using Singularity Theory, in Wakayama M, Anderssen RS, Cheng J, Fukumoto Y, McKibbin R, Polthier K, Takagi T, Toh K-C, The Impact of Applications on Mathematics, Springer-Verlag, Berlin, 2014. |

Start Year | 2013 |

Description | Collaboration - University of Tokyo |

Organisation | Swiss National Supercomputer Centre (CSCS) |

Country | Switzerland |

Sector | Academic/University |

PI Contribution | Collaboration with University of Tokyo. Research on the META project led to collaborative visit to groups in Tokyo & Kyushu, reciprocal visit by student: development of collaborative publications has begun. |

Collaborator Contribution | Mathematical expertise & problems. |

Impact | Chattopadhyay A, Carr H, Duke DJ, Geng Z, Saeki O, Multivariate Topology Simplification and Measure Persistence, Computational Geometry: Theory & Algorithms 58:1-24 (2017). Sakurai D, Saeki O, Carr H, Wu, Hsiang-Yun, Yamamoto T, Duke D, Takahashi S, Interactive Visualization for Singular Fibers of Functions f:R3->R2, IEEE VisWeek 2015 (IEEE Transactions on Visualization and Computer Graphics 22(1): 945-954 (2016)). Saeki O, Takahashi S, Sakurai D, Wu H-Y, Kikuchi K, Carr H, Duke D, Visualizing Multivariate Data Using Singularity Theory, in Wakayama M, Anderssen RS, Cheng J, Fukumoto Y, McKibbin R, Polthier K, Takagi T, Toh K-C, The Impact of Applications on Mathematics, Springer-Verlag, Berlin, 2014. |

Start Year | 2013 |

Description | Collaboration - University of Tokyo |

Organisation | University of Aizu |

Country | Japan |

Sector | Academic/University |

PI Contribution | Collaboration with University of Tokyo. Research on the META project led to collaborative visit to groups in Tokyo & Kyushu, reciprocal visit by student: development of collaborative publications has begun. |

Collaborator Contribution | Mathematical expertise & problems. |

Impact | Chattopadhyay A, Carr H, Duke DJ, Geng Z, Saeki O, Multivariate Topology Simplification and Measure Persistence, Computational Geometry: Theory & Algorithms 58:1-24 (2017). Sakurai D, Saeki O, Carr H, Wu, Hsiang-Yun, Yamamoto T, Duke D, Takahashi S, Interactive Visualization for Singular Fibers of Functions f:R3->R2, IEEE VisWeek 2015 (IEEE Transactions on Visualization and Computer Graphics 22(1): 945-954 (2016)). Saeki O, Takahashi S, Sakurai D, Wu H-Y, Kikuchi K, Carr H, Duke D, Visualizing Multivariate Data Using Singularity Theory, in Wakayama M, Anderssen RS, Cheng J, Fukumoto Y, McKibbin R, Polthier K, Takagi T, Toh K-C, The Impact of Applications on Mathematics, Springer-Verlag, Berlin, 2014. |

Start Year | 2013 |

Title | Fiber Surface Filters |

Description | Contributions to industry-leading vtk toolkit |

Type Of Technology | Software |

Year Produced | 2017 |

Open Source License? | Yes |

Impact | To be determined |

Title | Joint Contour Net |

Description | Joint Contour Net - code for multivariate topological analysis of data |

Type Of Technology | Software |

Year Produced | 2014 |

Open Source License? | Yes |

Impact | Adopted by other users |

URL | https://www.engineering.leeds.ac.uk/computing/research/cse/meta/ |

Title | vtk-m Parallel Contour Tree |

Description | Contribution of novel algorithm for contour trees to vtk-m toolkit through Los Alamos National Laboratory |

Type Of Technology | Software |

Year Produced | 2016 |

Open Source License? | Yes |

Impact | To be determined |