Workshop of CRC1456-WG 5 on June 14th, 2022
The first workshop will took place at the Convention Centre by the Observatory [Tagungszentrum an der Sternwarte - Geismar Landstr. 11b] on Tuesday, June 14th, 2022, see announcement pdf.
Thank you to all participants and the three speakers for interesting talks and intensive discussions!
Agenda
| from | to | speaker/title | comment |
|---|---|---|---|
| 13:00 | 13:05 | Christoph Lehrenfeld and Bernhard Schmitzer | |
| Welcome | |||
| 13:05 | 14:00 | Christian Himpe (WWU Münster) | chair: Christoph Lehrenfeld |
| Talk: MaRDI - Math, Data, Code | |||
| virtual presentation through BBB | |||
| SLIDES (abstract below) | |||
| incl. Discussion | |||
| 14:00 | 14:15 | Coffee Break | |
| 14:15 | 15:15 | Jean Feydy (INRIA Paris, HeKA team) | chair: Bernhard Schmitzer |
| Talk: Computational optimal transport: mature tools and open problems | |||
| SLIDES (abstract below) | |||
| Discussion and relation to CRC projects | |||
| 15:15 | 15:45 | Coffee Break | |
| 15:45 | 16:45 | Jonathan Eckstein (Rutgers University) | chair: Russell Luke |
| Talk: Parallel Computing and Optimization | |||
| (abstract below) | |||
| Discussion | |||
| 16:45 | Christoph Lehrenfeld and Bernhard Schmitzer | ||
| Closing Remarks |
After-workshop dinner
An after-workshop dinner is planned for 18:00 at LOKALneun.
Registration
Registration is finished but you are also invited to join spontaneously.
Abstracts of presentations
Christian Himpe, MaRDI - Math, Data, Code
Mathematical research produces and uses various kinds of research data, from integer sequences, over numerical data, to source codes. However, the findability, accessibility, interoperability and reusability (FAIR) of these data sources is neither given by default, nor enforced. This leads to unreprodicible computer-based experiments, gappy scientific documentations, and not least to inefficiencies due to "reinventing the wheel". Particularly for large-scale numerical computations, ensuring reproducibility is critical butremains largely unsolved.
To resolve these and similar issues across the sciences, the "Nationale Forschungsdaten Infrastruktur" (NFDI) association has been founded. For the field of mathematics specifically, the NFDI consortium "Mathematical Research Data Initiative" (MaRDI) was successfully funded. As a central part of MaRDI, the task-area "Scientific Computing" (TA2) represents the efforts of making data in scientific computing, computational science and engineering and numerics FAIR. The entailing practical measures of TA2 are presented, and MaRDI's overall contribution to help with these ever more pressing issues are detailed.
Jean Feydy (INRIA Paris, HeKA team), Computational optimal transport: mature tools and open problems
Optimal transport is a fundamental tool to deal with discrete and continuous distributions of points [1, 2]. We can understand it either as a generalization of sorting to spaces of dimension D>1, or as a nearest neighbor projection under a mass preservation constraint. Over the last decade, a sustained research effort on numerical foundations has led to a x1,000 speed-up for most transport-related computations. This has opened up a wide range of research directions in geometric data analysis, machine learning and computer graphics. This talk will discuss the consequences of these game-changing numerical advances from a user’s perspective. We will focus on:
- Mature libraries and software tools that can be used as of 2022 [3, 4, 5, 6, 7, 8], with a clear picture of the current state-of-the-art [9].
- New ranges of applications in 3D shape analysis, with a focus on population analysis [10] and pointluke cloud registration [11].
- Open problems that remain to be solved by experts in the field.
Joint work with: Minh-Hieu Do, Olga Mula-Hernandez, Marc Niethammer, Gabriel Peyré, Bernhard Schmitzer, Thibault Séjourné, Zhengyang Shen, Anna Song, Alain Trouvé, François-Xavier Vialard.
References:
- [1] G. Peyré and M. Cuturi. Computational optimal transport. https://optimaltransport.github.io/book/
- [2] J. Feydy. Geometric data analysis, beyond convolutions. https://www.jeanfeydy.com/geometric data analysis.pdf
- [3] R. Flamary et al. Python Optimal Transport. https://pythonot.github.io/
- [4] M. Cuturi et al. Optimal Transport Tools. https://ott-jax.readthedocs.io/
- [5] Alice INRIA team. Geogram software. http://alice.loria.fr/software/geogram
- [6] B. Schmitzer. MultiScale-OT toolbox. https://bernhard-schmitzer.github.io/MultiScaleOT
- [7] Q. Mérigot et al. PyMongeAmpere. https://github.com/mrgt/PyMongeAmpere
- [8] J. Feydy. GeomLoss. https://www.kernel-operations.io/geomloss/
- [9] J. Feydy et al. Optimal Transport benchmarks. https://optimal-transport-benchmarks.com/
- [10] A. Song. Generation of tubular and membranous shape textures with curvature functionals. SIAM Journal of Mathematical Imaging and Vision (2022).
- [11] Z. Shen et al. Accurate point cloud registration with robust optimal transport. NeurIPS 2021.
Jonathan Eckstein, Parallel Computing and Optimization
Parallel computing is a common tool in science and engineering. It is now common for large universities and government labs to own distributed HPC computing system with tens of thousands of processor cores, running applications involving simulation of appliations such protein folding, fluid flow, structure performance, and neural network training. Other kinds of numerical computing have lagged behind in their use of large-scale parallel computing. In my field, numerical optimization, the potential of parallel computing has not been fully exploited. The most popular and robust optimization solver codes do not scale well beyond dozens of cores for some applications, and exhibit poor scaling after just a handful of cores in other cases. There are several reasons why, including the difficulty of parallelizing the central numerical operations in standard linear and nonlinear optimization algorithms, commitment to deterministic execution patterns, and programming difficulties. Languages and compilers for developing parallel algorithms have displayed little meaningful evolution in the last few decades even as hardware capabilities have soared; in fact, they have arguably devolved since the 1990's.However, the potential for using parallel computing in optimization remains.
This talk will examine how numerical optimization solvers could be able to effectively take advantage of parallel computing, focusing on first-order methods for continuous optimization and search methods for discrete and nonconvex optimization. For truly challenging applications, it may be possible to combine such approaches. It will also discuss the potential obstacles and how they might be overcome.