Dear Colleagues,

HPC and scalable software pose numerous challenges to developers: achieving scalable performance, numerical accuracy and bitwise reproducibility, and ease of programming diverse architectures through tools (OpenMP, OpenACC, etc.) as well as advanced compiler techniques to allow application programmers to exploit current and future hardware designs without exposing them to machine-specific details. New fields like performance engineering are emerging to address some of these issues. However, without strong mathematical foundations and a commitment to codesign all components of software and hardware systems, such problems will increase and expand in complexity. Is it time to reformulate operating systems and memory management? Can existing languages still work in an era where massive HPC and AI data structures like arrays (tensors) must map automatically to a vast range of distributed memory designs? How can numerical accuracy and bitwise reproducibility be guaranteed on systems where the arithmetic and language standards do not specify bitwise-reproducible rounding? This Special Issue will address all those who are using mathematical foundations to seek portable and scalable ways to optimize hardware utilization without sacrificing programmer productivity, who use co-design to guarantee performance and accuracy, and who seek verifications of design. We can prove semantic designs, but can we prove operational designs? Can we prove that the outcome of two compilers on a single machine are equivalent? Can we predict performance automatically (using source code and a sufficient description of target hardware) to reduce the need for “ninja programmers”? What issues should be studied that have been avoided to solve these problems? This Special Issues encourages visionary scientists to submit papers in the areas of mathematical foundations to address all topics above, as well as the following:

(1) Numerical accuracy and bitwise reproducibility across machines and languages;

(2) Verification of semantic and operational designs;

(3) Domain-specific machines, operating systems, and languages;

(4) Software tools to automate scalable performance on HPC machines without sacrificing reproducibility.

Prof. Dr. Lenore Mullin
Prof. Dr. John L. Gustafson
Guest Editors

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Title: When does large scale computing with data generate value
Authors: Kartik B. Ariyur
Affiliation: School of Mechanical Engineering Purdue University
Abstract: Large scale computing problems of engineering relevance, whether it is search, constraint satisfaction, estimation, or resource allocation, can all be mapped into problems of optimization. Large dimensional resource allocation problems are extremely sensitive to uncertainties in model parameters. The algorithms that estimate these parameters, including neural networks or GANs need the data to be sampled fast enough, stationarity of some properties such as chess rules, constraints on the underlying physical system, observability of physical state, identifiability of parameters, and have adequate signal to noise ratio for reliable performance. Various factors, including uncertainties in components and operating environment, noise, disturbances, corruption or disruption of measurements by competing stake holders prevent one or more of these conditions from being satisfied. This can make the estimation or resource allocation problems ill posed, or greatly increase the energy and time required for obtaining good data. Similarly, many large data sets collected by industry or governments may not satisfy these properties and assuming they do could generate catastrophic results.