# Technical Reports

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Technical Report Can the United States Maintain Its Leadership in High-Performance Computing? - A report from the ASCAC Subcommittee on American Competitiveness and Innovation to the ASCR Office

(Office of Scientific and Technical Information (OSTI), 2023-06-28) Dongarra, Jack; Deelman, Ewa; Hey, Tony; Matsuoka, Satoshi; Sarakar, Vivek; Bell, Greg; Foster, Ian; Keyes, David E.; Kranzlmueller, Dieter; Lucas, Bob; Parker, Lynne; Shalf, John; Stanzione, Dan; Stevens, Rick; Yelick, Katherine; King Abdullah University of Science and Technology (KAUST), Thuwal (Saudi Arabia); Applied Mathematics and Computational Science Program; Extreme Computing Research Center; Office of the President; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division; Univ. of Tennessee, Knoxville, TN (United States); Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States); Univ. of Southern California, Los Angeles, CA (United States); Science and Technology Facilities Council (STFC), Oxford (United Kingdom). Rutherford Appleton Lab. (RAL); RIKEN, Saitama (Japan); Tokyo Institute of Technology (Japan); Georgia Inst. of Technology, Atlanta, GA (United States); Corelight; Argonne National Laboratory (ANL), Argonne, IL (United States); Univ. of Chicago, IL (United States); Leibniz Supercomputing Centre; Ludwig Maximilian Univ. of Munich, Munich (Germany); Ansys; Univ. of Tennessee, Knoxville, TN (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States); Texas Advanced Computing Center, Austin, TX (United States); Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)Technical Report Complex systems engineering theory is a scientific theory

(2022-12-26) Feron, Eric; CEMSEComplex systems engineering and associated challenges become increasingly important for the well-being and safety of our society of humans. Motivated by this push towards ever more complex systems of all sizes, spectacular failures, and decades of questioning in a variety of contexts and endeavors, this report presents a theory of complex systems engineering, that is, a scientific theory in which an engineered system can be seen as a validated scientific hypothesis arising from a convergent mix of mathematical and validated experimental constructs. In its simplest form, a complex engineered system is a manufactured, validated scientific hypothesis arising from a mathematical theorem similar to those found in theoretical physics. This observation provides suggestions for improving system design, especially system architecture, by leveraging advanced mathematical and / or scientific concepts. In return, mathematicians and computer scientists can benefit from this bridge to engineering by bringing to bear many of their automated and manual theorem proving techniques to help with the design of complex systems. Clear classifications of what is "hard" and what is "easy" in mathematical proofs can instantaneously map onto similar appreciations for system design and its reliance on engineers’ creativity. Last, understanding system design from the mathematical-scientific viewpoint can help the system engineer think more maturely about organizing the multitude of tasks required by systems engineering. Following these conclusions, a limited set of experiments is presented to try and invalidate the proposed systems engineering theory by confronting it to existing educational programs in systems engineering in the United States of America. Concurrent with these invalidation efforts, this report argues that there is a significant lack of education in basic mathematics and/or engineering science in many systems engineering programs. Such weaknesses challenge the current and future industrial efficiency of all corporate or government institutions engaged in the pursuit of complex engineered systems excellence.

Technical Report Complex systems engineering theory is a scientific theory

(2022-12-05) Feron, Eric; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division; Electrical and Computer Engineering ProgramThe proper design of complex engineering systems is what allows corporations and nations to distinguish themselves in a global competition for technical excellence and economic well-being. After quickly reviewing the central elements of systems engineering, we map all of them onto concepts of mathematics such as theorems and proofs, and onto scientific theories. This mapping allows the protagonists of complex systems engineering and design to map existing techniques from one field to the others; it provides a surprising number of suggestions for improving system design, especially system architecture, by leveraging advanced mathematical and / or scientific concepts in a productive way. In return, mathematicians and computer scientists can benefit from this bridge by bringing to bear many of their automated theorem provers to help with the design of complex systems. Clear classifications of what is "hard" and what is "easy" in mathematical proofs can instantaneously map onto similar appreciations for system design and its reliance on engineers’ creativity. Last, understanding system design from the mathematical-scientific viewpoint can help the system engineer think more maturely about organizing the multitude of tasks required by systems engineering.

Meeting Report Nonstandard Finite Element Methods

(European Mathematical Society - EMS - Publishing House GmbH, 2022-03-14) Boffi, Daniele; Carstensen, Carsten; Ern, Alexandre; Hu, Jun; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division; Humboldt-Universität zu Berlin, Germany; CERMICS - ENPC, Marne-La-Vallée, France; Peking University, Beijing, ChinaFinite element methodologies dominate the computational approaches for the solution to partial differential equations and nonstandard finite element schemes most urgently require mathematical insight in their design. The hybrid workshop vividly enlightened and discussed innovative nonconforming and polyhedral methods, discrete complex-based finite element methods for tensor-problems, fast solvers and adaptivity, as well as applications to challenging ill-posed and nonlinear problems.

Technical Report Accelerating Geostatistical Modeling and Prediction With Mixed-Precision Computations: A High-Productivity Approach with PaRSEC

(2021-05-06) Abdulah, Sameh; Cao, Qinglei; Pei, Yu; Bosilca, George; Dongarra, Jack; Genton, Marc G.; Keyes, David E.; Ltaief, Hatem; Sun, Ying; Computer, Electrical and Mathematical Sciences and Engineering Division (CEMSE); The Innovative Computing Laboratory, University of Tennessee, Knoxville, TN 37996, USGeostatistical modeling, one of the prime motivating applications for exascale computing, is a technique for predicting desired quantities from geographically distributed data, based on statistical models and optimization of parameters. Spatial data is assumed to possess properties of stationarity or non-stationarity via a kernel fitted to a covariance matrix. A primary workhorse of stationary spatial statistics is Gaussian maximum log-likelihood estimation (MLE), whose central data structure is a dense, symmetric positive definite covariance matrix of dimension of the number of correlated observations. Two essential operations in MLE are the application of the inverse and evaluation of the determinant of the covariance matrix. These can be rendered through the Cholesky decomposition and triangular solution. In this contribution, we reduce the precision of weakly correlated locations to single- or half- precision based on distance. We thus exploit mathematical structure to migrate MLE to a three-precision approximation that takes advantage of contemporary architectures offering BLAS3-like operations in a single instruction that are extremely fast for reduced precision. We illustrate application-expected accuracy worthy of double-precision from a majority half-precision computation, in a context where uniform single precision is by itself insufficient. In tackling the complexity and imbalance caused by the mixing of three precisions, we deploy the PaRSEC runtime system. PaRSEC delivers on-demand casting of precisions while orchestrating tasks and data movement in a multi-GPU distributed-memory environment within a tile-based Cholesky factorization. Application-expected accuracy is maintained while achieving up to 1.59 by mixing FP64/FP32 operations on 1536 nodes of HAWK or 4096 nodes of Shaheen-II, and up to 2.64X by mixing FP64/FP32/FP16 operations on 128 nodes of Summit, relative to FP64-only operations, This translates into up to 4.5, 4.7, and 9.1 (mixed) PFlop/s sustained performance, respectively, demonstrating a synergistic combination of exascale architecture, dynamic runtime software, and algorithmic adaptation applied to challenging environmental problems.