Applied Mathematics Research for Exascale Computing
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97 MATHEMATICS AND COMPUTING↗
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Computer Science Research Institute (CSRI) Summer Proceedings 2013
The Computer Science Research Institute (CSRI) brings university faculty and students to Sandia National Laboratories for focused collaborative research on computer science, computational science, and mathematics problems that are critical to the mission of the laboratories, the Department of Energy, and the United States. The CSRI provides a mechanism by which university researchers learn about and impact national— and global—scale problems while simultaneously bringing new ideas from the academic research community to bear on these important problems. A key component of CSRI programs over the last decade has been an active and productive summer program where students from around the country conduct internships at CSRI. Each student is paired with a Sandia staff member who serves as technical advisor and mentor. The goals of the summer program are to expose the students to research in mathematical and computer sciences at Sandia and to conduct a meaningful and impactful summer research project with their Sandia mentor. Every effort is made to align summer projects with the student's research objectives and all work is coordinated with the ongoing research activities of the Sandia mentor in alignment with Sandia technical thrusts. For the 2013 CSRI Proceedings, research articles have been organized into the following broad technical focus areas — Computational Mathematics and Algorithms, Combinatorial Algorithms and Visualization, Advanced Architectures and Systems Software, Computational Applications — which are well aligned with Sandia's strategic thrusts in computer and information sciences.
97 MATHEMATICS AND COMPUTING↗
ASCR@40: Four Decades of Department of Energy Leadership in Advanced Scientific Computing Research
Throughout its long history, the Office of Advanced Scientific Computing Research (ASCR) has built the critical technologies to ensure U.S. leadership in energy science and national security. It has made its parent agency, the Department of Energy (DOE) and its Office of Science, the world’s recognized leader in computational science. ASCR’s stated mission is “to discover, develop, and deploy computational and networking capabilities to analyze, model, simulate, and predict complex phenomena important to the DOE.” To accomplish this goal, ASCR oversees a large complex of computing and networking facilities and is responsible for procuring, deploying and operating high-performance computing (HPC), networking and storage resources; conducting basic research in mathematics and computer science; developing and sustaining a large body of software; and collaborating with other Office of Science programs, academia and industry. ASCR’s computational science leadership has a long history, predating even DOE’s inception. Applied mathematics and advanced computing were both elements of the Manhattan Project’s Theoretical Division. In the 1950s, DOE’s predecessor, the Atomic Energy Commission, created a mathematics program to develop and apply digital computing by supporting researchers at universities and AEC laboratories. Several organizational and name changes later, this program would grow and become ASCR.
97 MATHEMATICS AND COMPUTING↗
ASCR@40: Highlights and Impacts of ASCR’s Programs
A report compiled by the ASCAC Subcommittee on the 40-year history of ASCR for the U.S. Department of Energy’s Office of Advanced Scientific Computing Research. The Office of Advanced Scientific Computing Research (ASCR) sits within the Office of Science in the Department of Energy (DOE). Per their web pages, “the mission of the ASCR program is to discover, develop, and deploy computational and networking capabilities to analyze, model, simulate, and predict complex phenomena important to the DOE.” This succinct statement encompasses a wide range of responsibilities for computing and networking facilities; for procuring, deploying, and operating high performance computing, networking, and storage resources; for basic research in mathematics and computer science; for developing and sustaining a large body of software; and for partnering with organizations across the Office of Science and beyond. While its mission statement may seem very contemporary, the roots of ASCR are quite deep—long predating the creation of DOE. Applied mathematics and advanced computing were both elements of the Theoretical Division of the Manhattan Project. In the early 1950s, the Manhattan Project scientist and mathematician John von Neumann, then a commissioner for the AEC (Atomic Energy Commission), advocated for the creation of a Mathematics program to support the continued development and applications of digital computing. Los Alamos National Laboratory (LANL) scientist John Pasta created such a program to fund researchers at universities and AEC laboratories. Under several organizational name changes, this program has persisted ever since, and would eventually grow to become ASCR.
97 MATHEMATICS AND COMPUTING↗
PNNL Strategic Goods Testbed: A Data Library for Illicit Nuclear Trafficking
Pacific Northwest National Laboratory (PNNL) has put significant effort into nonproliferation activities as an institution, both in terms of the classical nuclear material focused approach and in the examination of other strategic goods necessary to implement a nuclear program. To assist in these efforts, several projects in the Analysis in Motion (AIM) and Signature Discovery (SDI) Initiatives at PNNL are developing machine learning methodology for human-computer interaction in real time environments to assist analysts in this domain. All of these technical projects require access to data – whether it is in terms of detector data, shipping records, financial information, company relations, or other communications. The first question that mathematical and computational researchers come up with when asked to build analyst assist or automated tools is “What does the data look like? ” They become frustrated when basic questions like this can not be easily answered and this can have the effect of pushing researchers away from the nuclear trafficking domain, especially in strategic commodity and export control areas where data sets can not easily be generated through standard experimental techniques. For small projects that are building a proof of concept for their methodology, obtaining this data can be arduous and expensive. To relieve the burden of data collection from these projects and grow a lab-wide capability, the Strategic Goods Testbed Team has taken over data collection and placed subscriptions and access to flat data files in a centralized location so that all projects can benefit from these items. We have collected shipping data in the form of PIERS records, judicial information about export control cases, NAC data on the nuclear fuel industry, and financial data from Dun and Bradstreet and our data sets are continuing to expand. With a single access agreement, researchers in data-mining and other fields can utilize all of the records that have been downloaded, make requests through subscription services, and interact with other researchers through our interface. Our testbed team provides more than a simply static repository by working with researchers to refine their data needs and insure data quality as well as quantity. We are currently working with laboratory and initiative specific management to examine effective ways for continuing data growth and sustainability.
data capability↗
Computational Math Problems for a Clean Energy Future
Cutting edge computational mathematics are ubiquitous in renewable energy research. Problems in resilient and reliable electric grid operations, infrastructure planning, wind farm yaw control, and more demand sophisticated and scalable computational tools that enable the transition of renewable energy technologies from proof of concept to deployment into our energy system. The mission of the Computational Science Center at NREL is to lead the lab's efforts to solve energy challenges using high-performance computing (HPC), computational science, applied mathematics, scientific data management, visualization, and informatics. In this poster, we provide a short overview of three areas of computational mathematics research at NREL: wind power scenario generation for stochastic grid operations and infrastructure planning, improved rational function approximations for electromagnetic transients codes, and wind farm yaw control using a combination of the Alternating Direction Method of Multipliers (ADMM) and reinforcement learning (RL). Increasing penetrations of renewable energy into power grids motivate the investigation of new approaches to characterizing uncertainty for five-minute economic dispatch problems. Similarly, as the penetration of distributed energy resources on power grids increases, it becomes important to revisit our methods of modelling transient phenomena, i.e. electromagnetic transients programs. Finally, the combination of ADMM and RL for wind farm yaw control presented here can potentially increase the efficiency of the deployed distributed controllers by orders of magnitude.
ADMM↗
Workshop on Manufacturing and Integration Challenges for Analog and Neuromorphic Computing
The U.S. Department of Energy’s (DOE’s) Advanced Manufacturing Office (AMO) held its third virtual workshop on Semiconductor R&D for Energy Efficiency on August 11-13, 2021. This public workshop – titled “Manufacturing and Integration Challenges for Analog and Neuromorphic Computing” – brought together more than 180 leading scientific and technical experts to identify challenges and opportunities to improve manufacturing capabilities for analog and neuromorphic computing architectures to significantly increase energy efficiency of microelectronic devices. The workshop featured perspectives of researchers from national laboratories, universities, government agencies, and industry with expertise in novel and emerging devices, processes, and metrology and characterization. This workshop is intended to inform an AMO research, development, demonstration, and deployment (RDD&D) plan to significantly reduce semiconductor energy use by 2030. It was co-sponsored by the Semiconductor Research Corporation (SRC) and the DOE Office of Science’s Advanced Scientific Computing Research (ASCR).
97 MATHEMATICS AND COMPUTING↗
2025 Workshop on Envisioning Frontiers in AI and Computing for Biological Research: Position Papers
This workshop aims to identify key research directions for transforming biology using artificial intelligence (AI), machine learning (ML) and computational methods to facilitate the discovery of new behaviors, mechanisms, and designs of biological processes relevant to DOE missions, underpinning a broader U.S. bioeconomy. By developing novel AI/ML technologies to analyze and interpret complex biological data, researchers can organize and simulate biological processes at various scales as well as advance predictive understanding and manipulation of biological systems. This integration of computation, experimentation, and next-generation experimental technologies can lead to discoveries in new biological behaviors and mechanisms relevant to DOE missions. The focus is on how advanced computational and mathematical methods can impact this mission by exploring digital twins, foundation models, automated laboratory experiments, modeling of complex living systems, and data-driven approaches for the biodesign of plants and microbial systems. While data management is important, it is not the primary focus of this workshop, which will assess the current state, trends, and AI/ML challenges at the interface between biology and computational science to identify opportunities for high-impact research at their intersection. The goal is to define research needs and opportunities that align with biological sciences, computational sciences, and applied mathematics research.
59 BASIC BIOLOGICAL SCIENCES↗
LLNL Response to the DOE ASCR RFI, "Stewardship of Software for Scientific and High-Performance Computing"
For decades, Lawrence Livermore National Laboratory (LLNL) has been engaged in significant research, development, and support for software to enable scientific computing and, particularly, the use of high performance computing (HPC) in the NNSA mission space. In particular, the move in the mid-1990’s to simulation as a leading component of stockpile stewardship through the ASCI and the successor ASC programs, as well as the need for reliable data acquisition and control software for the National Ignition Facility, have been important drivers in building expertise in production-quality software development at LLNL. LLNL has also been a leader in the DOE SciDAC FASTMath Institute and the DOE Exascale Computing Project (ECP), both of which have striven to make scientific computing software – in particular, the enabling technologies underpinning simulation capabilities – more widely adopted and sustainable. As such, we believe that our experience can inform the broader goal of software stewardship for scientific and high-performance computing. LLNL strongly supports the formation of a new DOE ASCR program element in software stewardship and sustainment. Historically, DOE ASCR has funded applied mathematics and computer science research that has led to the development of important new capabilities and algorithms that are expressed as artifacts in research software. Such frameworks, libraries, and tools have seldom been directly funded to address the important issues of code maintenance, documentation, robustness, and community building. Software engineering and support have typically been done on the side in support of the ASCR-driven research products. DOE funding priorities have been slow to recognize that good software engineering, the kind that ensures research investments have more adoption and longevity, requires significant resources. Based upon our experiences, we have prepared this response to highlight the concerns and issues we believe to be important as DOE ASCR considers its role in scientific software stewardship. We believe that role is important and will require a significant investment of new funding to legitimately support the technologies past and future DOE ASCR investments have and will produce to facilitate their uptake and adoption in the broader scientific computing community. Following a summary of our involvement in scientific software development, the remainder our response is organized around the nine topics specifically identified in the RFI.
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Fast Approximate Union Volume in High Dimensions with Line Samples
The classical problem of calculating the volume of the union of d-dimensional balls is known as "Union Volume." We present line-sampling approximation algorithms for Union Volume. Our methods may be extended to other Boolean operations, such as setminus; or to other shapes, such as hyper-rectangles. The deterministic, exact approaches for Union Volume do not scale well to high dimensions. However, we adapt several of these exact approaches to approximation algorithms based on sampling. We perform local sampling within each ball using lines. We have several variations, depending on how the overlapping volume is partitioned, and depending on whether radial, axis-aligned, or other line patterns are used. Our variations fall within the family of Monte Carlo sampling, and hence have about the same theoretical convergence rate, 1 /$\sqrt{M}$, where M is the number of samples. In our limited experiments, line-sampling proved more accurate per unit work than point samples, because a line sample provides more information, and the analytic equation for a sphere makes the calculation almost as fast. We performed a limited empirical study of the efficiency of these variations. We suggest a more extensive study for future work. We speculate that different ball arrangements, differentiated by the distribution of overlaps in terms of volume and degree, will benefit the most from patterns of line samples that preferentially capture those overlaps. Acknowledgement We thank Karl Bringman for explaining his BF-ApproxUnion (ApproxUnion) algorithm [3] to us. We thank Josiah Manson for pointing out that spoke darts oversample the center and we might get a better answer by uniform sampling. We thank Vijay Natarajan for suggesting random chord sampling. The authors are grateful to Brian Adams, Keith Dalbey, and Vicente Romero for useful technical discussions. This work was sponsored by the Laboratory Directed Research and Development (LDRD) Program at Sandia National Laboratories. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research (ASCR), Applied Mathematics Program. Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA0003525.
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EpiCast: Simulating Epidemics with Extreme Detail
In early 2020, COVID-19 swept the globe. Governments attempted to “flatten the curve” through business shutdowns and stay-at-home orders, but the United States was hit hard. By the end of March, mere months after the virus first emerged in humans 7,000 miles away, the U.S. had recorded 192,300 cases and 5,300 deaths. While this unprecedented disaster sent shockwaves through every level of society and clouded an uncertain future, state and local governments turned to computational and mathematical epidemiology researchers to help formulate intervention strategies to limit the spread of the disease. Traditional forecasting models provided a reasonable understanding of how the near future was likely to look, but local policy makers and public health communities still struggled to understand how potential mitigations ought to be implemented. Decision makers needed a way to measure the impact of their policy choices—they needed better technology. EpiCast answered the call, bringing urgently needed answers to policymakers grappling with how to adjust school and business schedules. EpiCast is modeling software that generates a synthetic, representative population to simulate infectious disease transmission in the United States with extreme detail and granularity. The software models human behavior combined with community-specific information to provide a fine-grained preview of the effect of potential mitigation strategies for decision makers.
60 APPLIED LIFE SCIENCES↗
Introducing Enabling Computational Tools to the Climate Sciences: Multi-Resolution Climate Modeling with Adaptive Cubed-Sphere Grids
The research investigates and advances strategies how to bridge the scale discrepancies between local, regional and global phenomena in climate models without the prohibitive computational costs of global cloud-resolving simulations. In particular, the research explores new frontiers in computational geoscience by introducing high-order Adaptive Mesh Refinement (AMR) techniques into climate research. AMR and statically-adapted variable-resolution approaches represent an emerging trend for atmospheric models and are likely to become the new norm in future-generation weather and climate models. The research advances the understanding of multi-scale interactions in the climate system and showcases a pathway how to model these interactions effectively with advanced computational tools, like the Chombo AMR library developed at the Lawrence Berkeley National Laboratory. The research is interdisciplinary and combines applied mathematics, scientific computing and the atmospheric sciences. In this research project, a hierarchy of high-order atmospheric models on cubed-sphere computational grids have been developed that serve as an algorithmic prototype for the finite-volume solution-adaptive Chombo-AMR approach. The foci of the investigations have lied on the characteristics of both static mesh adaptations and dynamically-adaptive grids that can capture flow fields of interest like tropical cyclones. Six research themes have been chosen. These are (1) the introduction of adaptive mesh refinement techniques into the climate sciences, (2) advanced algorithms for nonhydrostatic atmospheric dynamical cores, (3) an assessment of the interplay between resolved-scale dynamical motions and subgrid-scale physical parameterizations, (4) evaluation techniques for atmospheric model hierarchies, (5) the comparison of AMR refinement strategies and (6) tropical cyclone studies with a focus on multi-scale interactions and variable-resolution modeling. The results of this research project demonstrate significant advances in all six research areas. The major conclusions are that statically-adaptive variable-resolution modeling is currently becoming mature in the climate sciences, and that AMR holds outstanding promise for future-generation weather and climate models on high-performance computing architectures.
58 GEOSCIENCES↗
Multiscale Design of Advanced Materials based on Hybrid Ab Initio and Quasicontinuum Methods
This project united researchers from mathematics, chemistry, computer science, and engineering for the development of new multiscale methods for the design of materials. Our approach was highly interdisciplinary, but it had two unifying themes: first, we utilized modern mathematical ideas about change-of-scale and state-of-the-art numerical analysis to develop computational methods and codes to solve real multiscale problems of DOE interest; and, second, we took very seriously the need for quantum mechanics-based atomistic forces, and based our methods on fast solvers of chemically accurate methods.
97 MATHEMATICS AND COMPUTING↗
Compact representation and long-time extrapolation of real-time data for quantum systems using the ESPRIT algorithm
Representing real-time data as a sum of complex exponentials provides a compact form that enables both denoising and extrapolation. As a fully data-driven method, the Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) algorithm is agnostic to the underlying physical equations, making it broadly applicable to various observables and experimental or numerical setups. In this work, we consider applications of the ESPRIT algorithm primarily to extend real-time dynamical data from simulations of quantum systems. We evaluate ESPRIT's performance in the presence of noise and compare it to other extrapolation methods. We demonstrate its ability to extract information from short-time dynamics to reliably predict long-time behavior and determine the minimum time interval required for accurate results. We discuss how this insight can be leveraged in numerical methods that propagate quantum systems in time, and we show how ESPRIT can predict infinite-time values of dynamical observables, offering a purely data-driven approach to characterizing quantum phases.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
The Heidelberg Laureate Forum on the moving frontier between mathematics and computer science
Here, young and early-career researchers at the 2016 Heidelberg Laureate Forum discuss how the frontier between mathematics and computer science is shifting, what the future promises, and the implications the frontier's shape and dynamics will have on both fields.
97 MATHEMATICS AND COMPUTING↗
Complex Systems Research at LANL [Slides]
Mathematics, computer science, and technologies required to extract information, knowledge, and insight from data. Thrust leverages advances in theory, algorithms, and the exponential growth of high–performance computing to accelerate the integrative and predictive capability of the scientific method. Thrust focuses on the integration of LANL capabilities for understanding, prediction, and design of complex, natural and engineered systems.
97 MATHEMATICS AND COMPUTING↗
Direct interpolative construction of the discrete Fourier transform as a matrix product operator
The quantum Fourier transform (QFT), which can be viewed as a reindexing of the discrete Fourier transform (DFT), has been shown to be compressible as a low-rank matrix product operator (MPO) or quantized tensor train (QTT) operator. However, the original proof of this fact does not furnish a construction of the MPO with a guaranteed error bound. Meanwhile, the existing practical construction of this MPO, based on the compression of a quantum circuit, is not as efficient as possible. We present a simple closed-form construction of the QFT MPO using the interpolative decomposition, with guaranteed near-optimal compression error for a given rank. This construction can speed up the application of the QFT and the DFT, respectively, in quantum circuit simulations and QTT applications. We also connect our interpolative construction to the approximate quantum Fourier transform (AQFT) by demonstrating that the AQFT can be viewed as an MPO constructed using a different interpolation scheme.
97 MATHEMATICS AND COMPUTING↗
Advancing Understanding of Fission Gas Behavior in Nuclear Fuel through Leadership Class Computing
This report describes the outcome of the pilot SciDAC project jointly funded by the DOE Office of Nuclear Energy and the DOE Office of Science, Advanced Scientific Computing Research to advance understanding of fission gas behavior in nuclear fuel. The computational approach involved utilizing both a bottom up and top down multiscale materials modeling to evaluate the processes of xenon fission gas diffusion, xenon clustering and precipitation and the mechanisms of fission gas resolution by energetic fission fragments in uranium dioxide nuclear fuel. The computer science and applied mathematics research activities were focused on optimizing the uranium – oxygen – xenon interatomic potential implementation in the LAMMPS molecular dynamics code for large-scale simulations of fission gas resolution, in addition to improvements in visualization of accelerated molecular dynamics simulations and performance optimization of the Xolotl continuum cluster dynamics with a new grouping scheme to reduce the computational cost of modeling very large fission gas bubbles containing more than 10,000 xenon atoms. The most impactful result from this project stems from a systematic series of atomistic molecular dynamics to evaluate fission gas resolution from xenon bubbles that, combined with the fission product yields and consideration of electron-phonon coupling, informed a first principles model that predicts the magnitude of fission gas resolution in good agreement with empirical estimates.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗