Numerical Algorithms, Frameworks, and Scalable Technologies for Extreme-Scale Computing

• Applicant: Professor Dr. Matthias Bollhöfer
• Subject Area: Computer Architecture, Embedded and Massively Parallel Systems
• Term: since 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 470857344

Computing has been disruptive to scientific domains that rely on computational models and data to discover new knowledge and form decisions. With the explosion of Big Data, we are faced with the ever-increasing size, variability, and uncertainty of the datasets. Some of the most challenging problems in data-driven science involve understanding the interactions between millions or billions of variables. The vast quantity, veracity, velocity, and variety of data are challenging high-performance sparse numerical methods and software for extreme-scale computing. Progress in research in scientific computing algorithms and software has been tightly linked to progress in microprocessor technology and high-performance programming technology. We are now embarking on the extreme-scale computing era which will revolutionize the architectural stack. It will also require research on optimized mathematical software libraries according to the device characteristics with novel numerical algorithms and data science applications that exploit them. How can we reconcile sustainable advances in sparse linear algebra and nonlinear optimization for new applications in data analytics while at the same time prepare for the anticipated sea-change looming in a 20-year hardware horizon? We seek answers through computational methods that resolve fundamental challenges imposed by large-scale analytics, deep analysis, and precise predictions by advancing the next generation of sparse numerical methods. Our algorithms rely on the innovative coupling of sparse numerical linear algebra and nonlinear optimization methods for data-intensive applications. These methods require the development of robust approximation methods under the condition of extreme-scale computing. This includes scientific libraries providing high-quality, reusable software components for constructing applications, as well as improved robustness and portability. These developments will be driven by research on mathematical software, extreme-scale computing and an effort to push these developments toward applications. The computation of functions of matrix inverses goes beyond the requirements in solving linear systems or eigenvalue problems and has not yet been addressed in most of the research projects on massively parallel architectures. It is expected that the techniques will prove important in many data-driven applications and will provide basic tools for applications for high performance computing and engineering problems. Novel, scalable software engineered to facilitate broader public use will be made available to the research and industrial community. Our numerical algorithms and mathematical software libraries are capable of leveraging emerging hardware paradigms and are applicable to applications such as finance, biology, health, and many more. we will shed light on applications on nanoelectronic device simulation, and high-dimensional partial correlation estimations in genomics applications.

• DFG Programme: Research Grants
• International Connection: Switzerland
• Cooperation Partner: Professor Dr. Olaf Schenk