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

Computing has been disruptive to all scientific domains that increasingly rely on computational models and data to discover new knowledge and form decisions. With the explosion of Big Data, we are now 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 even thousands of millions of variables. The vast quantity, veracity, velocity, and variety of data are challenging classical high-performance 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 in the process of embarking on the extreme-scale computing era which will revolutionize the architectural stack in a holistic fashion. 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 domains in data analytics while at the same time prepare for the anticipated sea-change looming in a twenty-year hardware horizon as well? We seek answers to these questions through computational methods that resolve fundamental challenges imposed by large-scale analytics, deep analysis, and precise predictions by advancing and preparing the foundation for the next generation of sparsified numerical methods. Our algorithms rely on the innovative coupling of sparsified numerical linear algebra and nonlinear optimization methods for data-intensive applications. The inherently deterministic character of these methods, when coupled with high communication demands, requires the development of robust approximation methods under the condition of extreme-scale computational science. This includes scientific libraries providing high-quality, reusable software components for constructing applications, as well as improved robustness ad portability. These developments will be driven by research on mathematical software, extreme-scale computing and an effort to push these developments toward applications. The focus on the computation of functions of matrix inverse entries presents a new dimension of numerical methods, since it goes beyond the classical 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 developed by this will prove important in many of the other data-driven applications and will also provide basic tools for most of the applications for high performance computing (HPC) science 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 a wide variety of existing applications such as finance, biology, health sciences, and many more. In particular, we will shed light on applications on nanoelectronic device simulation, and high-dimensional partial correlation estimations in genomics applications.